Original 5.40

1 files changed, 1932 insertions, 0 deletions

diff --git a/hacks/xlyap.c b/hacks/xlyap.c
new file mode 100644
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--- /dev/null
+++ b/hacks/xlyap.c
@@ -0,0 +1,1932 @@
+/* Lyap - calculate and display Lyapunov exponents */
+
+/* Written by Ron Record (rr@sco) 03 Sep 1991 */
+
+/* The idea here is to calculate the Lyapunov exponent for a periodically
+ * forced logistic map (later i added several other nonlinear maps of the unit
+ * interval). In order to turn the 1-dimensional parameter space of the
+ * logistic map into a 2-dimensional parameter space, select two parameter
+ * values ('a' and 'b') then alternate the iterations of the logistic map using
+ * first 'a' then 'b' as the parameter. This program accepts an argument to
+ * specify a forcing function, so instead of just alternating 'a' and 'b', you
+ * can use 'a' as the parameter for say 6 iterations, then 'b' for 6 iterations
+ * and so on. An interesting forcing function to look at is abbabaab (the
+ * Morse-Thue sequence, an aperiodic self-similar, self-generating sequence).
+ * Anyway, step through all the values of 'a' and 'b' in the ranges you want,
+ * calculating the Lyapunov exponent for each pair of values. The exponent
+ * is calculated by iterating out a ways (specified by the variable "settle")
+ * then on subsequent iterations calculating an average of the logarithm of
+ * the absolute value of the derivative at that point. Points in parameter
+ * space with a negative Lyapunov exponent are colored one way (using the
+ * value of the exponent to index into a color map) while points with a
+ * non-negative exponent are colored differently.
+ *
+ * The algorithm was taken from the September 1991 Scientific American article
+ * by A. K. Dewdney who gives credit to Mario Markus of the Max Planck
+ * Institute for its creation. Additional information and ideas were gleaned
+ * from the discussion on alt.fractals involving Stephen Hall, Ed Kubaitis,
+ * Dave Platt and Baback Moghaddam. Assistance with colormaps and spinning
+ * color wheels and X was gleaned from Hiram Clawson. Rubber banding code was
+ * adapted from an existing Mandelbrot program written by Stacey Campbell.
+ */
+
+#define LYAP_PATCHLEVEL 4
+#define LYAP_VERSION "#(@) lyap 2.3 2/20/92"
+
+#include <assert.h>
+#include <math.h>
+
+#include "screenhack.h"
+#include "yarandom.h"
+#include "hsv.h"
+
+#undef countof
+#define countof(x) (sizeof((x))/sizeof((*x)))
+
+#ifndef HAVE_JWXYZ
+# include <X11/cursorfont.h> 
+#endif
+
+static const char *xlyap_defaults [] = {
+  ".background:         black",
+  ".foreground:         white",
+  ".lowrez:             true",
+  "*fpsSolid:		true",
+  "*randomize:          true",
+  "*builtin:            -1",
+  "*minColor:           1",
+  "*maxColor:           256",
+  "*dwell:              50",
+  "*useLog:             false",
+  "*colorExponent:      1.0",
+  "*colorOffset:        0",
+  "*randomForce:        ",              /* 0.5 */
+  "*settle:             50",
+  "*minA:               2.0",
+  "*minB:               2.0",
+  "*wheels:             7",
+  "*function:           10101010",
+  "*forcingFunction:    abbabaab",
+  "*bRange:             ",              /* 2.0 */
+  "*startX:             0.65",
+  "*mapIndex:           ",              /* 0 */
+  "*outputFile:         ",
+  "*beNegative:         false",
+  "*rgbMax:             65000",
+  "*spinLength:         256",
+  "*show:               false",
+  "*aRange:             ",              /* 2.0 */
+  "*delay:              10000",
+  "*linger:             5",
+  "*colors:             200",
+#ifdef HAVE_MOBILE
+  "*ignoreRotation:     True",
+#endif
+  0
+};
+
+static XrmOptionDescRec xlyap_options [] = {
+  { "-randomize", ".randomize", XrmoptionNoArg, "true" },
+  { "-builtin",   ".builtin",   XrmoptionSepArg, 0 },
+  { "-C", ".minColor",          XrmoptionSepArg, 0 },   /* n */
+  { "-D", ".dwell",             XrmoptionSepArg, 0 },   /* n */
+  { "-L", ".useLog",            XrmoptionNoArg, "true" },
+  { "-M", ".colorExponent",     XrmoptionSepArg, 0 },   /* r */
+  { "-O", ".colorOffset",       XrmoptionSepArg, 0 },   /* n */
+  { "-R", ".randomForce",       XrmoptionSepArg, 0 },   /* p */
+  { "-S", ".settle",            XrmoptionSepArg, 0 },   /* n */
+  { "-a", ".minA",              XrmoptionSepArg, 0 },   /* r */
+  { "-b", ".minB",              XrmoptionSepArg, 0 },   /* n */
+  { "-c", ".wheels",            XrmoptionSepArg, 0 },   /* n */
+  { "-F", ".function",          XrmoptionSepArg, 0 },   /* 10101010 */
+  { "-f", ".forcingFunction",   XrmoptionSepArg, 0 },   /* abbabaab */
+  { "-h", ".bRange",            XrmoptionSepArg, 0 },   /* r */
+  { "-i", ".startX",            XrmoptionSepArg, 0 },   /* r */
+  { "-m", ".mapIndex",          XrmoptionSepArg, 0 },   /* n */
+  { "-o", ".outputFile",        XrmoptionSepArg, 0 },   /* filename */
+  { "-p", ".beNegative",        XrmoptionNoArg, "true" },
+  { "-r", ".rgbMax",            XrmoptionSepArg, 0 },   /* n */
+  { "-s", ".spinLength",        XrmoptionSepArg, 0 },   /* n */
+  { "-v", ".show",              XrmoptionNoArg, "true" },
+  { "-w", ".aRange",            XrmoptionSepArg, 0 },   /* r */
+  { "-delay", ".delay",         XrmoptionSepArg, 0 },   /* delay */
+  { "-linger", ".linger",       XrmoptionSepArg, 0 },   /* linger */
+  { 0, 0, 0, 0 }
+};
+
+
+#define ABS(a)  (((a)<0) ? (0-(a)) : (a) )
+#define Min(x,y) ((x < y)?x:y)
+#define Max(x,y) ((x > y)?x:y)
+
+#ifdef SIXTEEN_COLORS
+# define MAXPOINTS  128
+# ifdef BIGMEM
+#  define MAXFRAMES 4
+# else  /* !BIGMEM */
+#  define MAXFRAMES 2
+# endif /* !BIGMEM */
+# define MAXCOLOR 16
+#else  /* !SIXTEEN_COLORS */
+# define MAXPOINTS  256
+# ifdef BIGMEM
+#  define MAXFRAMES 8
+# else  /* !BIGMEM */
+#  define MAXFRAMES 2
+# endif /* !BIGMEM */
+# define MAXCOLOR 256
+#endif /* !SIXTEEN_COLORS */
+
+
+#define MAXINDEX 64
+#define FUNCMAXINDEX 16
+#define MAXWHEELS 7
+#define NUMMAPS 5
+#define NBUILTINS 22
+
+#ifndef TRUE
+# define TRUE 1
+# define FALSE 0
+#endif
+
+
+typedef struct {
+  int x, y;
+} xy_t;
+
+#if 0
+typedef struct {
+  int start_x, start_y;
+  int last_x, last_y;
+} rubber_band_data_t;
+#endif
+
+typedef struct {
+# ifndef HAVE_JWXYZ
+  Cursor band_cursor;
+# endif
+  double p_min, p_max, q_min, q_max;
+/*  rubber_band_data_t rubber_band;*/
+} image_data_t;
+
+typedef struct points_t {
+  XPoint data[MAXCOLOR][MAXPOINTS];
+  int npoints[MAXCOLOR];
+} points_t;
+
+
+typedef double (*PFD)(double,double);
+
+/* #### What was this for?  Everything was drawn twice, to the window and 
+   to this, and this was never displayed! */
+/*#define BACKING_PIXMAP*/
+
+struct state {
+  Display *dpy;
+  Screen *screen;
+  Visual *visual;
+  Colormap cmap;
+
+  unsigned long foreground, background;
+
+  Window canvas;
+  int delay, linger;
+
+  unsigned int maxcolor, startcolor, mincolindex;
+  int color_offset;
+  int dwell, settle;
+  int width, height, xposition, yposition;
+
+  points_t Points;
+/*  image_data_t rubber_data;*/
+
+  GC Data_GC[MAXCOLOR]/*, RubberGC*/;
+  PFD map, deriv;
+
+  int aflag, bflag, wflag, hflag, Rflag;
+
+  int   maxindex;
+  int   funcmaxindex;
+  double  min_a, min_b, a_range, b_range, minlyap;
+  double  max_a, max_b;
+  double  start_x, lyapunov, a_inc, b_inc, a, b;
+  int   numcolors, numfreecols, lowrange;
+  xy_t  point;
+#ifdef BACKING_PIXMAP
+  Pixmap  pixmap;
+#endif
+/*  XColor  Colors[MAXCOLOR];*/
+  double  *exponents[MAXFRAMES];
+  double  a_minimums[MAXFRAMES], b_minimums[MAXFRAMES];
+  double  a_maximums[MAXFRAMES], b_maximums[MAXFRAMES];
+  double  minexp, maxexp, prob;
+  int     expind[MAXFRAMES], resized[MAXFRAMES];
+  int     numwheels, force, Force, negative;
+  int     rgb_max, nostart, stripe_interval;
+  int     save, show, useprod, spinlength;
+  int     maxframe, frame, dorecalc, mapindex, run;
+  char    *outname;
+
+  int sendpoint_index;
+
+  int   forcing[MAXINDEX];
+  int   Forcing[FUNCMAXINDEX];
+
+  int reset_countdown;
+
+  int ncolors;
+  XColor colors[MAXCOLOR];
+};
+
+
+static const double pmins[NUMMAPS] = { 2.0, 0.0, 0.0, 0.0, 0.0 };
+static const double pmaxs[NUMMAPS] = { 4.0, 1.0, 6.75, 6.75, 16.0 };
+static const double amins[NUMMAPS] = { 2.0, 0.0, 0.0, 0.0, 0.0 };
+static const double aranges[NUMMAPS] = { 2.0, 1.0, 6.75, 6.75, 16.0 };
+static const double bmins[NUMMAPS] = { 2.0, 0.0, 0.0, 0.0, 0.0 };
+static const double branges[NUMMAPS] = { 2.0, 1.0, 6.75, 6.75, 16.0 };
+
+/****************************************************************************/
+
+/* callback function declarations
+ */
+
+static double logistic(double,double);
+static double circle(double,double);
+static double leftlog(double,double);
+static double rightlog(double,double);
+static double doublelog(double,double);
+static double dlogistic(double,double);
+static double dcircle(double,double);
+static double dleftlog(double,double);
+static double drightlog(double,double);
+static double ddoublelog(double,double);
+
+static const PFD Maps[NUMMAPS] = { logistic, circle, leftlog, rightlog, 
+                                   doublelog };
+static const PFD Derivs[NUMMAPS] = { dlogistic, dcircle, dleftlog, 
+                                     drightlog, ddoublelog };
+
+
+/****************************************************************************/
+
+/* other function declarations
+ */
+
+static void resize(struct state *);
+/*static void Spin(struct state *);*/
+static void show_defaults(struct state *);
+/*static void StartRubberBand(struct state *, image_data_t *, XEvent *);
+static void TrackRubberBand(struct state *, image_data_t *, XEvent *);
+static void EndRubberBand(struct state *, image_data_t *, XEvent *);*/
+/*static void CreateXorGC(struct state *);*/
+static void InitBuffer(struct state *);
+static void BufferPoint(struct state *, int color, int x, int y);
+static void FlushBuffer(struct state *);
+static void init_data(struct state *);
+static void init_color(struct state *);
+static void parseargs(struct state *);
+static void Clear(struct state *);
+static void setupmem(struct state *);
+static int complyap(struct state *);
+static Bool Getkey(struct state *, XKeyEvent *);
+static int sendpoint(struct state *, double expo);
+/*static void save_to_file(struct state *);*/
+static void setforcing(struct state *);
+static void check_params(struct state *, int mapnum, int parnum);
+static void usage(struct state *);
+static void Destroy_frame(struct state *);
+static void freemem(struct state *);
+static void Redraw(struct state *);
+static void redraw(struct state *, double *exparray, int index, int cont);
+static void recalc(struct state *);
+/*static void SetupCorners(XPoint *, image_data_t *);
+static void set_new_params(struct state *, image_data_t *);*/
+static void go_down(struct state *);
+static void go_back(struct state *);
+static void go_init(struct state *);
+static void jumpwin(struct state *);
+static void print_help(struct state *);
+static void print_values(struct state *);
+
+
+/****************************************************************************/
+
+
+/* complyap() is the guts of the program. This is where the Lyapunov exponent
+ * is calculated. For each iteration (past some large number of iterations)
+ * calculate the logarithm of the absolute value of the derivative at that
+ * point. Then average them over some large number of iterations. Some small
+ * speed up is achieved by utilizing the fact that log(a*b) = log(a) + log(b).
+ */
+static int
+complyap(struct state *st)
+{
+  int i, bindex;
+  double total, prod, x, dx, r;
+
+  if (st->maxcolor > MAXCOLOR)
+    abort();
+
+  if (!st->run)
+    return TRUE;
+  st->a += st->a_inc;
+  if (st->a >= st->max_a) {
+    if (sendpoint(st, st->lyapunov) == TRUE)
+      return FALSE;
+    else {
+      FlushBuffer(st);
+      /*      if (savefile)
+              save_to_file(); */
+      return TRUE;
+    }
+  }
+  if (st->b >= st->max_b) {
+    FlushBuffer(st);
+    /*    if (savefile)
+          save_to_file();*/
+    return TRUE;
+  }
+  prod = 1.0;
+  total = 0.0;
+  bindex = 0;
+  x = st->start_x;
+  r = (st->forcing[bindex]) ? st->b : st->a;
+#ifdef MAPS
+  findex = 0;
+  map = Maps[st->Forcing[findex]];
+#endif
+  for (i=0;i<st->settle;i++) {     /* Here's where we let the thing */
+    x = st->map (x, r);  /* "settle down". There is usually */
+    if (++bindex >= st->maxindex) { /* some initial "noise" in the */
+      bindex = 0;    /* iterations. How can we optimize */
+      if (st->Rflag)      /* the value of settle ??? */
+        setforcing(st);
+    }
+    r = (st->forcing[bindex]) ? st->b : st->a;
+#ifdef MAPS
+    if (++findex >= funcmaxindex)
+      findex = 0;
+    map = Maps[st->Forcing[findex]];
+#endif
+  }
+#ifdef MAPS
+  deriv = Derivs[st->Forcing[findex]];
+#endif
+  if (st->useprod) {      /* using log(a*b) */
+    for (i=0;i<st->dwell;i++) {
+      x = st->map (x, r);
+      dx = st->deriv (x, r); /* ABS is a macro, so don't be fancy */
+      dx = ABS(dx);
+      if (dx == 0.0) /* log(0) is nasty so break out. */
+        {
+          i++;
+          break;
+        }
+      prod *= dx;
+      /* we need to prevent overflow and underflow */
+      if ((prod > 1.0e12) || (prod < 1.0e-12)) {
+        total += log(prod);
+        prod = 1.0;
+      }
+      if (++bindex >= st->maxindex) {
+        bindex = 0;
+        if (st->Rflag)
+          setforcing(st);
+      }
+      r = (st->forcing[bindex]) ? st->b : st->a;
+#ifdef MAPS
+      if (++findex >= funcmaxindex)
+        findex = 0;
+      map = Maps[st->Forcing[findex]];
+      deriv = Derivs[st->Forcing[findex]];
+#endif
+    }
+    total += log(prod);
+    st->lyapunov = (total * M_LOG2E) / (double)i;   
+  }
+  else {        /* use log(a) + log(b) */
+    for (i=0;i<st->dwell;i++) {
+      x = st->map (x, r);
+      dx = st->deriv (x, r); /* ABS is a macro, so don't be fancy */
+      dx = ABS(dx);
+      if (x == 0.0)  /* log(0) check */
+        {
+          i++;
+          break;
+        }
+      total += log(dx);
+      if (++bindex >= st->maxindex) {
+        bindex = 0;
+        if (st->Rflag)
+          setforcing(st);
+      }
+      r = (st->forcing[bindex]) ? st->b : st->a;
+#ifdef MAPS
+      if (++findex >= funcmaxindex)
+        findex = 0;
+      map = Maps[st->Forcing[findex]];
+      deriv = Derivs[st->Forcing[findex]];
+#endif
+    }
+    st->lyapunov = (total * M_LOG2E) / (double)i;
+  }
+
+  if (sendpoint(st, st->lyapunov) == TRUE)
+    return FALSE;
+  else {
+    FlushBuffer(st);
+    /*    if (savefile)
+          save_to_file();*/
+    return TRUE;
+  }
+}
+
+static double
+logistic(double x, double r)        /* the familiar logistic map */
+{
+  return(r * x * (1.0 - x));
+}
+
+static double
+dlogistic(double x, double r)       /* the derivative of logistic map */
+{
+  return(r - (2.0 * r * x));
+}
+
+static double
+circle(double x, double r)        /* sin() hump or sorta like the circle map */
+{
+  return(r * sin(M_PI * x));
+}
+
+static double
+dcircle(double x, double r)       /* derivative of the "sin() hump" */
+{
+  return(r * M_PI * cos(M_PI * x));
+}
+
+static double
+leftlog(double x, double r)       /* left skewed logistic */
+{
+  double d;
+
+  d = 1.0 - x;
+  return(r * x * d * d);
+}
+
+static double
+dleftlog(double x, double r)    /* derivative of the left skewed logistic */
+{
+  return(r * (1.0 - (4.0 * x) + (3.0 * x * x)));
+}
+
+static double
+rightlog(double x, double r)    /* right skewed logistic */
+{
+  return(r * x * x * (1.0 - x));
+}
+
+static double
+drightlog(double x, double r)    /* derivative of the right skewed logistic */
+{
+  return(r * ((2.0 * x) - (3.0 * x * x)));
+}
+
+static double
+doublelog(double x, double r)    /* double logistic */
+{
+  double d;
+
+  d = 1.0 - x;
+  return(r * x * x * d * d);
+}
+
+static double
+ddoublelog(double x, double r)   /* derivative of the double logistic */
+{
+  double d;
+
+  d = x * x;
+  return(r * ((2.0 * x) - (6.0 * d) + (4.0 * x * d)));
+}
+
+static void
+init_data(struct state *st)
+{
+  st->numcolors = get_integer_resource (st->dpy, "colors", "Integer");
+  if (st->numcolors < 2)
+    st->numcolors = 2;
+  if (st->numcolors > st->maxcolor)
+    st->numcolors = st->maxcolor;
+  st->numfreecols = st->numcolors - st->mincolindex;
+  st->lowrange = st->mincolindex - st->startcolor;
+  st->a_inc = st->a_range / (double)st->width;
+  st->b_inc = st->b_range / (double)st->height;
+  st->point.x = -1;
+  st->point.y = 0;
+  st->a = /*st->rubber_data.p_min = */st->min_a;
+  st->b = /*st->rubber_data.q_min = */st->min_b;
+/*  st->rubber_data.p_max = st->max_a;
+  st->rubber_data.q_max = st->max_b;*/
+  if (st->show)
+    show_defaults(st);
+  InitBuffer(st);
+}
+
+#if 0
+static void
+hls2rgb(int hue_light_sat[3],
+        int rgb[3])             /*      Each in range [0..65535]        */
+{
+  unsigned short r, g, b;
+  hsv_to_rgb((int) (hue_light_sat[0] / 10),             /* 0-3600 -> 0-360 */
+             (int) ((hue_light_sat[2]/1000.0) * 64435), /* 0-1000 -> 0-65535 */
+             (int) ((hue_light_sat[1]/1000.0) * 64435), /* 0-1000 -> 0-65535 */
+             &r, &g, &b);
+  rgb[0] = r;
+  rgb[1] = g;
+  rgb[2] = b;
+}
+#endif /* 0 */
+
+
+static void
+init_color(struct state *st)
+{
+  int i;
+  if (st->ncolors)
+    free_colors (st->screen, st->cmap, st->colors, st->ncolors);
+  st->ncolors = st->maxcolor;
+  make_smooth_colormap(st->screen, st->visual, st->cmap,
+                       st->colors, &st->ncolors, True, NULL, True);
+
+  for (i = 0; i < st->maxcolor; i++) {
+    if (! st->Data_GC[i]) {
+      XGCValues gcv;
+      gcv.background = BlackPixelOfScreen(st->screen);
+      st->Data_GC[i] = XCreateGC(st->dpy, st->canvas, GCBackground, &gcv);
+    }
+    XSetForeground(st->dpy, st->Data_GC[i],
+                   st->colors[((int) ((i / ((float)st->maxcolor)) *
+                                      st->ncolors))].pixel);
+  }
+}
+
+
+static void
+parseargs(struct state *st)
+{
+  int i;
+  int bindex=0, findex;
+  char *s, *ch;
+
+  st->map = Maps[0];
+  st->deriv = Derivs[0];
+  st->maxexp=st->minlyap; st->minexp= -1.0 * st->minlyap;
+
+  st->mincolindex = get_integer_resource(st->dpy, "minColor", "Integer");
+  st->dwell = get_integer_resource(st->dpy, "dwell", "Integer");
+#ifdef MAPS
+  {
+    char *optarg = get_string_resource(st->dpy, "function", "String");
+    funcmaxindex = strlen(optarg);
+    if (funcmaxindex > FUNCMAXINDEX)
+      usage();
+    ch = optarg;
+    st->Force++;
+    for (findex=0;findex<funcmaxindex;findex++) {
+      st->Forcing[findex] = (int)(*ch++ - '0');;
+      if (st->Forcing[findex] >= NUMMAPS)
+        usage();
+    }
+  }
+#endif
+  if (get_boolean_resource(st->dpy, "useLog", "Boolean"))
+    st->useprod=0;
+
+  st->minlyap=ABS(get_float_resource(st->dpy, "colorExponent", "Float"));
+  st->maxexp=st->minlyap;
+  st->minexp= -1.0 * st->minlyap;
+
+  st->color_offset = get_integer_resource(st->dpy, "colorOffset", "Integer");
+
+  st->maxcolor=ABS(get_integer_resource(st->dpy, "maxColor", "Integer"));
+  if ((st->maxcolor - st->startcolor) <= 0)
+    st->startcolor = get_pixel_resource(st->dpy, st->cmap,
+                                        "background", "Background");
+  if ((st->maxcolor - st->mincolindex) <= 0) {
+    st->mincolindex = 1;
+    st->color_offset = 0;
+  }
+
+  s = get_string_resource(st->dpy, "randomForce", "Float");
+  if (s && *s) {
+    st->prob=atof(s); st->Rflag++; setforcing(st);
+  }
+
+  st->settle = get_integer_resource(st->dpy, "settle", "Integer");
+
+#if 0
+  s = get_string_resource(st->dpy, "minA", "Float");
+  if (s && *s) {
+    st->min_a = atof(s);
+    st->aflag++;
+  }
+  
+  s = get_string_resource(st->dpy, "minB", "Float");
+  if (s && *s) {
+    st->min_b=atof(s); st->bflag++;
+  }
+#else
+  st->min_a = get_float_resource (st->dpy, "minA", "Float");
+  st->aflag++;
+  st->min_b = get_float_resource (st->dpy, "minB", "Float");
+  st->bflag++;
+#endif
+
+  
+  st->numwheels = get_integer_resource(st->dpy, "wheels", "Integer");
+
+  s = get_string_resource(st->dpy, "forcingFunction", "String");
+  if (s && *s) {
+    st->maxindex = strlen(s);
+    if (st->maxindex > MAXINDEX)
+      usage(st);
+    ch = s;
+    st->force++;
+    while (bindex < st->maxindex) {
+      if (*ch == 'a')
+        st->forcing[bindex++] = 0;
+      else if (*ch == 'b')
+        st->forcing[bindex++] = 1;
+      else
+        usage(st);
+      ch++;
+    }
+  }
+
+  s = get_string_resource(st->dpy, "bRange", "Float");
+  if (s && *s) {
+    st->b_range = atof(s);
+    st->hflag++;
+  }
+
+  st->start_x = get_float_resource(st->dpy, "startX", "Float");
+
+  s = get_string_resource(st->dpy, "mapIndex", "Integer");
+  if (s && *s) {
+    st->mapindex=atoi(s);
+    if ((st->mapindex >= NUMMAPS) || (st->mapindex < 0))
+      usage(st);
+    st->map = Maps[st->mapindex];
+    st->deriv = Derivs[st->mapindex];
+    if (!st->aflag)
+      st->min_a = amins[st->mapindex];
+    if (!st->wflag)
+      st->a_range = aranges[st->mapindex];
+    if (!st->bflag)
+      st->min_b = bmins[st->mapindex];
+    if (!st->hflag)
+      st->b_range = branges[st->mapindex];
+    if (!st->Force)
+      for (i=0;i<FUNCMAXINDEX;i++)
+        st->Forcing[i] = st->mapindex;
+  }
+
+  st->outname = get_string_resource(st->dpy, "outputFile", "Integer");
+
+  if (get_boolean_resource(st->dpy, "beNegative", "Boolean"))
+    st->negative--;
+
+  st->rgb_max = get_integer_resource(st->dpy, "rgbMax", "Integer");
+  st->spinlength = get_integer_resource(st->dpy, "spinLength", "Integer");
+  st->show = get_boolean_resource(st->dpy, "show", "Boolean");
+
+  s = get_string_resource(st->dpy, "aRange", "Float");
+  if (s && *s) {
+    st->a_range = atof(s); st->wflag++;
+  }
+
+  st->max_a = st->min_a + st->a_range;
+  st->max_b = st->min_b + st->b_range;
+
+  st->a_minimums[0] = st->min_a; st->b_minimums[0] = st->min_b;
+  st->a_maximums[0] = st->max_a; st->b_maximums[0] = st->max_b;
+
+  if (st->Force)
+    if (st->maxindex == st->funcmaxindex)
+      for (findex=0;findex<st->funcmaxindex;findex++)
+        check_params(st, st->Forcing[findex],st->forcing[findex]);
+    else
+      fprintf(stderr, "Warning! Unable to check parameters\n");
+  else
+    check_params(st, st->mapindex,2);
+}
+
+static void
+check_params(struct state *st, int mapnum, int parnum)
+{
+
+  if (parnum != 1) {
+    if ((st->max_a > pmaxs[mapnum]) || (st->min_a < pmins[mapnum])) {
+      fprintf(stderr, "Warning! Parameter 'a' out of range.\n");
+      fprintf(stderr, "You have requested a range of (%f,%f).\n",
+              st->min_a,st->max_a);
+      fprintf(stderr, "Valid range is (%f,%f).\n",
+              pmins[mapnum],pmaxs[mapnum]);
+    }
+  }
+  if (parnum != 0) {
+    if ((st->max_b > pmaxs[mapnum]) || (st->min_b < pmins[mapnum])) {
+      fprintf(stderr, "Warning! Parameter 'b' out of range.\n");
+      fprintf(stderr, "You have requested a range of (%f,%f).\n",
+              st->min_b,st->max_b);
+      fprintf(stderr, "Valid range is (%f,%f).\n",
+              pmins[mapnum],pmaxs[mapnum]);
+    }
+  }
+}
+
+static void
+usage(struct state *st)
+{
+  fprintf(stderr,"lyap [-BLs][-W#][-H#][-a#][-b#][-w#][-h#][-x xstart]\n");
+  fprintf(stderr,"\t[-M#][-S#][-D#][-f string][-r#][-O#][-C#][-c#][-m#]\n");
+#ifdef MAPS
+  fprintf(stderr,"\t[-F string]\n");
+#endif
+  fprintf(stderr,"\tWhere: -C# specifies the minimum color index\n");
+  fprintf(stderr,"\t       -r# specifies the maxzimum rgb value\n");
+  fprintf(stderr,"\t       -u displays this message\n");
+  fprintf(stderr,"\t       -a# specifies the minimum horizontal parameter\n");
+  fprintf(stderr,"\t       -b# specifies the minimum vertical parameter\n");
+  fprintf(stderr,"\t       -w# specifies the horizontal parameter range\n");
+  fprintf(stderr,"\t       -h# specifies the vertical parameter range\n");
+  fprintf(stderr,"\t       -D# specifies the dwell\n");
+  fprintf(stderr,"\t       -S# specifies the settle\n");
+  fprintf(stderr,"\t       -H# specifies the initial window height\n");
+  fprintf(stderr,"\t       -W# specifies the initial window width\n");
+  fprintf(stderr,"\t       -O# specifies the color offset\n");
+  fprintf(stderr,"\t       -c# specifies the desired color wheel\n");
+  fprintf(stderr,"\t       -m# specifies the desired map (0-4)\n");
+  fprintf(stderr,"\t       -f aabbb specifies a forcing function of 00111\n");
+#ifdef MAPS
+  fprintf(stderr,"\t       -F 00111 specifies the function forcing function\n");
+#endif
+  fprintf(stderr,"\t       -L indicates use log(x)+log(y) rather than log(xy)\n");
+  fprintf(stderr,"\tDuring display :\n");
+  fprintf(stderr,"\t       Use the mouse to zoom in on an area\n");
+  fprintf(stderr,"\t       e or E recalculates color indices\n");
+  fprintf(stderr,"\t       f or F saves exponents to a file\n");
+  fprintf(stderr,"\t       KJmn increase/decrease minimum negative exponent\n");
+  fprintf(stderr,"\t       r or R redraws\n");
+  fprintf(stderr,"\t       s or S spins the colorwheel\n");
+  fprintf(stderr,"\t       w or W changes the color wheel\n");
+  fprintf(stderr,"\t       x or X clears the window\n");
+  fprintf(stderr,"\t       q or Q exits\n");
+  exit(1);
+}
+
+static void
+Cycle_frames(struct state *st)
+{
+  int i;
+  for (i=0;i<=st->maxframe;i++)
+    redraw(st, st->exponents[i], st->expind[i], 1);
+}
+
+#if 0
+static void
+Spin(struct state *st)
+{
+  int i, j;
+  long tmpxcolor;
+
+  if (!mono_p) {
+    for (j=0;j<st->spinlength;j++) {
+      tmpxcolor = st->Colors[st->mincolindex].pixel;
+      for (i=st->mincolindex;i<st->numcolors-1;i++)
+        st->Colors[i].pixel = st->Colors[i+1].pixel;
+      st->Colors[st->numcolors-1].pixel = tmpxcolor;
+      XStoreColors(st->dpy, st->cmap, st->Colors, st->numcolors);
+    }
+    for (j=0;j<st->spinlength;j++) {
+      tmpxcolor = st->Colors[st->numcolors-1].pixel;
+      for (i=st->numcolors-1;i>st->mincolindex;i--)
+        st->Colors[i].pixel = st->Colors[i-1].pixel;
+      st->Colors[st->mincolindex].pixel = tmpxcolor;
+      XStoreColors(st->dpy, st->cmap, st->Colors, st->numcolors);
+    }
+  }
+}
+#endif
+
+static Bool
+Getkey(struct state *st, XKeyEvent *event)
+{
+  unsigned char key;
+  int i;
+  if (XLookupString(event, (char *)&key, sizeof(key), (KeySym *)0,
+                    (XComposeStatus *) 0) > 0) {
+
+    if (st->reset_countdown)
+      st->reset_countdown = st->linger;
+
+    switch (key) {
+    case '<': st->dwell /= 2; if (st->dwell < 1) st->dwell = 1; return True;
+    case '>': st->dwell *= 2; return True;
+    case '[': st->settle /= 2; if (st->settle < 1) st->settle = 1; return True;
+    case ']': st->settle *= 2; return True;
+    case 'd': go_down(st); return True;
+    case 'D': FlushBuffer(st); return True;
+    case 'e':
+    case 'E': FlushBuffer(st);
+      st->dorecalc = (!st->dorecalc);
+      if (st->dorecalc)
+        recalc(st);
+      else {
+        st->maxexp = st->minlyap; st->minexp = -1.0 * st->minlyap;
+      }
+      redraw(st, st->exponents[st->frame], st->expind[st->frame], 1);
+      return True;
+    case 'f':
+      /*  case 'F': save_to_file(); return True;*/
+    case 'i': if (st->stripe_interval > 0) {
+        st->stripe_interval--;
+        if (!mono_p) {
+          init_color(st);
+        }
+      }
+      return True;
+    case 'I': st->stripe_interval++;
+      if (!mono_p) {
+        init_color(st);
+      }
+      return True;
+    case 'K': if (st->minlyap > 0.05)
+        st->minlyap -= 0.05;
+      return True;
+    case 'J': st->minlyap += 0.05;
+      return True;
+    case 'm': st->mapindex++;
+      if (st->mapindex >= NUMMAPS)
+        st->mapindex=0;
+      st->map = Maps[st->mapindex];
+      st->deriv = Derivs[st->mapindex];
+      if (!st->aflag)
+        st->min_a = amins[st->mapindex];
+      if (!st->wflag)
+        st->a_range = aranges[st->mapindex];
+      if (!st->bflag)
+        st->min_b = bmins[st->mapindex];
+      if (!st->hflag)
+        st->b_range = branges[st->mapindex];
+      if (!st->Force)
+        for (i=0;i<FUNCMAXINDEX;i++)
+          st->Forcing[i] = st->mapindex;
+      st->max_a = st->min_a + st->a_range;
+      st->max_b = st->min_b + st->b_range;
+      st->a_minimums[0] = st->min_a; st->b_minimums[0] = st->min_b;
+      st->a_maximums[0] = st->max_a; st->b_maximums[0] = st->max_b;
+      st->a_inc = st->a_range / (double)st->width;
+      st->b_inc = st->b_range / (double)st->height;
+      st->point.x = -1;
+      st->point.y = 0;
+      st->a = /*st->rubber_data.p_min = */st->min_a;
+      st->b = /*st->rubber_data.q_min = */st->min_b;
+/*      st->rubber_data.p_max = st->max_a;
+      st->rubber_data.q_max = st->max_b;*/
+      Clear(st);
+      return True;
+    case 'M': if (st->minlyap > 0.005)
+        st->minlyap -= 0.005;
+      return True;
+    case 'N': st->minlyap += 0.005;
+      return True;
+    case 'p':
+    case 'P': st->negative = (!st->negative);
+      FlushBuffer(st); redraw(st, st->exponents[st->frame], 
+                              st->expind[st->frame], 1);
+      return True;
+    case 'r': FlushBuffer(st); redraw(st, st->exponents[st->frame], 
+                                      st->expind[st->frame], 1);
+      return True;
+    case 'R': FlushBuffer(st); Redraw(st); return True;
+    case 's':
+      st->spinlength=st->spinlength/2;
+#if 0
+    case 'S': if (!mono_p)
+        Spin(st);
+      st->spinlength=st->spinlength*2; return True;
+#endif
+    case 'u': go_back(st); return True;
+    case 'U': go_init(st); return True;
+    case 'v':
+    case 'V': print_values(st); return True;
+    case 'W': if (st->numwheels < MAXWHEELS)
+        st->numwheels++;
+      else
+        st->numwheels = 0;
+      if (!mono_p) {
+        init_color(st);
+      }
+      return True;
+    case 'w': if (st->numwheels > 0)
+        st->numwheels--;
+      else
+        st->numwheels = MAXWHEELS;
+      if (!mono_p) {
+        init_color(st);
+      }
+      return True;
+    case 'x': Clear(st); return True;
+    case 'X': Destroy_frame(st); return True;
+    case 'z': Cycle_frames(st); redraw(st, st->exponents[st->frame], 
+                                       st->expind[st->frame], 1);
+      return True;
+#if 0
+    case 'Z': while (!XPending(st->dpy)) Cycle_frames(st);
+      redraw(st, st->exponents[st->frame], st->expind[st->frame], 1); 
+      return True;
+#endif
+    case 'q':
+    case 'Q': exit(0); return True;
+    case '?':
+    case 'h':
+    case 'H': print_help(st); return True;
+    default:  return False;
+    }
+  }
+
+  return False;
+}
+
+/* Here's where we index into a color map. After the Lyapunov exponent is
+ * calculated, it is used to determine what color to use for that point.  I
+ * suppose there are a lot of ways to do this. I used the following : if it's
+ * non-negative then there's a reserved area at the lower range of the color
+ * map that i index into. The ratio of some "minimum exponent value" and the
+ * calculated value is used as a ratio of how high to index into this reserved
+ * range. Usually these colors are dark red (see init_color).  If the exponent
+ * is negative, the same ratio (expo/minlyap) is used to index into the
+ * remaining portion of the colormap (which is usually some light shades of
+ * color or a rainbow wheel). The coloring scheme can actually make a great
+ * deal of difference in the quality of the picture. Different colormaps bring
+ * out different details of the dynamics while different indexing algorithms
+ * also greatly effect what details are seen. Play around with this.
+ */
+static int
+sendpoint(struct state *st, double expo)
+{
+  double tmpexpo;
+
+  if (st->maxcolor > MAXCOLOR)
+    abort();
+
+#if 0
+  /* The relationship st->minexp <= expo <= maxexp should always be true. This
+     test enforces that. But maybe not enforcing it makes better pictures. */
+  if (expo < st->minexp)
+    expo = st->minexp;
+  else if (expo > maxexp)
+    expo = maxexp;
+#endif
+
+  st->point.x++;
+  tmpexpo = (st->negative) ? expo : -1.0 * expo;
+  if (tmpexpo > 0) {
+    if (!mono_p) {
+      st->sendpoint_index = (int)(tmpexpo*st->lowrange/st->maxexp);
+      st->sendpoint_index = ((st->sendpoint_index % st->lowrange) + 
+                             st->startcolor);
+    }
+    else
+      st->sendpoint_index = 0;
+  }
+  else {
+    if (!mono_p) {
+      st->sendpoint_index = (int)(tmpexpo*st->numfreecols/st->minexp);
+      st->sendpoint_index = ((st->sendpoint_index % st->numfreecols)
+                             + st->mincolindex);
+    }
+    else
+      st->sendpoint_index = 1;
+  }
+  BufferPoint(st, st->sendpoint_index, st->point.x, st->point.y);
+  if (st->save) {
+    if (st->frame > MAXFRAMES)
+      abort();
+    st->exponents[st->frame][st->expind[st->frame]++] = expo;
+  }
+  if (st->point.x >= st->width) {
+    st->point.y++;
+    st->point.x = 0;
+    if (st->save) {
+      st->b += st->b_inc;
+      st->a = st->min_a;
+    }
+    if (st->point.y >= st->height)
+      return FALSE;
+    else
+      return TRUE;
+  }
+  return TRUE;
+}
+
+
+static void
+resize(struct state *st)
+{
+  Window r;
+  int n, x, y;
+  unsigned int bw, d, new_w, new_h;
+
+  XGetGeometry(st->dpy,st->canvas,&r,&x,&y,&new_w,&new_h,&bw,&d);
+  if ((new_w == st->width) && (new_h == st->height))
+    return;
+  st->width = new_w; st->height = new_h;
+  XClearWindow(st->dpy, st->canvas);
+#ifdef BACKING_PIXMAP
+  if (st->pixmap)
+    XFreePixmap(st->dpy, st->pixmap);
+  st->pixmap = XCreatePixmap(st->dpy, st->canvas, st->width, st->height, d);
+#endif
+  st->a_inc = st->a_range / (double)st->width;
+  st->b_inc = st->b_range / (double)st->height;
+  st->point.x = -1;
+  st->point.y = 0;
+  st->run = 1;
+  st->a = /*st->rubber_data.p_min = */st->min_a;
+  st->b = /*st->rubber_data.q_min = */st->min_b;
+/*  st->rubber_data.p_max = st->max_a;
+  st->rubber_data.q_max = st->max_b;*/
+  freemem(st);
+  setupmem(st);
+  for (n=0;n<MAXFRAMES;n++)
+    if ((n <= st->maxframe) && (n != st->frame))
+      st->resized[n] = 1;
+  InitBuffer(st);
+  Clear(st);
+  Redraw(st);
+}
+
+static void
+redraw(struct state *st, double *exparray, int index, int cont)
+{
+  int i, x_sav, y_sav;
+
+  x_sav = st->point.x;
+  y_sav = st->point.y;
+
+  st->point.x = -1;
+  st->point.y = 0;
+
+  st->save=0;
+  for (i=0;i<index;i++)
+    sendpoint(st, exparray[i]);
+  st->save=1;
+
+  if (cont) {
+    st->point.x = x_sav;
+    st->point.y = y_sav;
+  }
+  else {
+    st->a = st->point.x * st->a_inc + st->min_a;
+    st->b = st->point.y * st->b_inc + st->min_b;
+  }
+  FlushBuffer(st);
+}
+
+static void
+Redraw(struct state *st)
+{
+  FlushBuffer(st);
+  st->point.x = -1;
+  st->point.y = 0;
+  st->run = 1;
+  st->a = st->min_a;
+  st->b = st->min_b;
+  st->expind[st->frame] = 0;
+  st->resized[st->frame] = 0;
+}
+
+static void
+recalc(struct state *st)
+{
+  int i;
+
+  st->minexp = st->maxexp = 0.0;
+  for (i=0;i<st->expind[st->frame];i++) {
+    if (st->exponents[st->frame][i] < st->minexp)
+      st->minexp = st->exponents[st->frame][i];
+    if (st->exponents[st->frame][i] > st->maxexp)
+      st->maxexp = st->exponents[st->frame][i];
+  }
+}
+
+static void
+Clear(struct state *st)
+{
+  XClearWindow(st->dpy, st->canvas);
+#ifdef BACKING_PIXMAP
+  XCopyArea(st->dpy, st->canvas, st->pixmap, st->Data_GC[0],
+            0, 0, st->width, st->height, 0, 0);
+#endif
+  InitBuffer(st);
+}
+
+static void
+show_defaults(struct state *st)
+{
+
+  printf("Width=%d  Height=%d  numcolors=%d  settle=%d  dwell=%d\n",
+         st->width,st->height,st->numcolors,st->settle,st->dwell);
+  printf("min_a=%f  a_range=%f  max_a=%f\n", st->min_a,st->a_range,st->max_a);
+  printf("min_b=%f  b_range=%f  max_b=%f\n", st->min_b,st->b_range,st->max_b);
+  printf("minlyap=%f  minexp=%f  maxexp=%f\n", st->minlyap,st->minexp,
+         st->maxexp);
+  exit(0);
+}
+
+#if 0
+static void
+CreateXorGC(struct state *st)
+{
+  XGCValues values;
+
+  values.foreground = st->foreground;
+  values.function = GXxor;
+  st->RubberGC = XCreateGC(st->dpy, st->canvas,
+                           GCForeground | GCFunction, &values);
+}
+
+static void
+StartRubberBand(struct state *st, image_data_t *data, XEvent *event)
+{
+  XPoint corners[5];
+
+  st->nostart = 0;
+  data->rubber_band.last_x = data->rubber_band.start_x = event->xbutton.x;
+  data->rubber_band.last_y = data->rubber_band.start_y = event->xbutton.y;
+  SetupCorners(corners, data);
+  XDrawLines(st->dpy, st->canvas, st->RubberGC,
+             corners, sizeof(corners) / sizeof(corners[0]), CoordModeOrigin);
+}
+
+static void
+SetupCorners(XPoint *corners, image_data_t *data)
+{
+  corners[0].x = data->rubber_band.start_x;
+  corners[0].y = data->rubber_band.start_y;
+  corners[1].x = data->rubber_band.start_x;
+  corners[1].y = data->rubber_band.last_y;
+  corners[2].x = data->rubber_band.last_x;
+  corners[2].y = data->rubber_band.last_y;
+  corners[3].x = data->rubber_band.last_x;
+  corners[3].y = data->rubber_band.start_y;
+  corners[4] = corners[0];
+}
+
+static void
+TrackRubberBand(struct state *st, image_data_t *data, XEvent *event)
+{
+  XPoint corners[5];
+  int xdiff, ydiff;
+
+  if (st->nostart)
+    return;
+  SetupCorners(corners, data);
+  XDrawLines(st->dpy, st->canvas, st->RubberGC,
+             corners, sizeof(corners) / sizeof(corners[0]), CoordModeOrigin);
+  ydiff = event->xbutton.y - data->rubber_band.start_y;
+  xdiff = event->xbutton.x - data->rubber_band.start_x;
+  data->rubber_band.last_x = data->rubber_band.start_x + xdiff;
+  data->rubber_band.last_y = data->rubber_band.start_y + ydiff;
+  if (data->rubber_band.last_y < data->rubber_band.start_y ||
+      data->rubber_band.last_x < data->rubber_band.start_x)
+    {
+      data->rubber_band.last_y = data->rubber_band.start_y;
+      data->rubber_band.last_x = data->rubber_band.start_x;
+    }
+  SetupCorners(corners, data);
+  XDrawLines(st->dpy, st->canvas, st->RubberGC,
+             corners, sizeof(corners) / sizeof(corners[0]), CoordModeOrigin);
+}
+
+static void
+EndRubberBand(struct state *st, image_data_t *data, XEvent *event)
+{
+  XPoint corners[5];
+  XPoint top, bot;
+  double delta, diff;
+
+  st->nostart = 1;
+  SetupCorners(corners, data);
+  XDrawLines(st->dpy, st->canvas, st->RubberGC,
+             corners, sizeof(corners) / sizeof(corners[0]), CoordModeOrigin);
+  if (data->rubber_band.start_x >= data->rubber_band.last_x ||
+      data->rubber_band.start_y >= data->rubber_band.last_y)
+    return;
+  top.x = data->rubber_band.start_x;
+  bot.x = data->rubber_band.last_x;
+  top.y = data->rubber_band.start_y;
+  bot.y = data->rubber_band.last_y;
+  diff = data->q_max - data->q_min;
+  delta = (double)top.y / (double)st->height;
+  data->q_min += diff * delta;
+  delta = (double)(st->height - bot.y) / (double)st->height;
+  data->q_max -= diff * delta;
+  diff = data->p_max - data->p_min;
+  delta = (double)top.x / (double)st->width;
+  data->p_min += diff * delta;
+  delta = (double)(st->width - bot.x) / (double)st->width;
+  data->p_max -= diff * delta;
+  set_new_params(st, data);
+}
+
+static void
+set_new_params(struct state *st, image_data_t *data)
+{
+  st->frame = (st->maxframe + 1) % MAXFRAMES;
+  if (st->frame > st->maxframe)
+    st->maxframe = st->frame;
+  st->a_range = data->p_max - data->p_min;
+  st->b_range = data->q_max - data->q_min;
+  st->a_minimums[st->frame] = st->min_a = data->p_min;
+  st->b_minimums[st->frame] = st->min_b = data->q_min;
+  st->a_inc = st->a_range / (double)st->width;
+  st->b_inc = st->b_range / (double)st->height;
+  st->point.x = -1;
+  st->point.y = 0;
+  st->run = 1;
+  st->a = st->min_a;
+  st->b = st->min_b;
+  st->a_maximums[st->frame] = st->max_a = data->p_max;
+  st->b_maximums[st->frame] = st->max_b = data->q_max;
+  st->expind[st->frame] = 0;
+  Clear(st);
+}
+#endif
+
+static void
+go_down(struct state *st)
+{
+  st->frame++;
+  if (st->frame > st->maxframe)
+    st->frame = 0;
+  jumpwin(st);
+}
+
+static void
+go_back(struct state *st)
+{
+  st->frame--;
+  if (st->frame < 0)
+    st->frame = st->maxframe;
+  jumpwin(st);
+}
+
+static void
+jumpwin(struct state *st)
+{
+  /*st->rubber_data.p_min =*/ st->min_a = st->a_minimums[st->frame];
+  /*st->rubber_data.q_min =*/ st->min_b = st->b_minimums[st->frame];
+  /*st->rubber_data.p_max =*/ st->max_a = st->a_maximums[st->frame];
+  /*st->rubber_data.q_max =*/ st->max_b = st->b_maximums[st->frame];
+  st->a_range = st->max_a - st->min_a;
+  st->b_range = st->max_b - st->min_b;
+  st->a_inc = st->a_range / (double)st->width;
+  st->b_inc = st->b_range / (double)st->height;
+  st->point.x = -1;
+  st->point.y = 0;
+  st->a = st->min_a;
+  st->b = st->min_b;
+  Clear(st);
+  if (st->resized[st->frame])
+    Redraw(st);
+  else
+    redraw(st, st->exponents[st->frame], st->expind[st->frame], 0);
+}
+
+static void
+go_init(struct state *st)
+{
+  st->frame = 0;
+  jumpwin(st);
+}
+
+static void
+Destroy_frame(struct state *st)
+{
+  int i;
+
+  for (i=st->frame; i<st->maxframe; i++) {
+    st->exponents[st->frame] = st->exponents[st->frame+1];
+    st->expind[st->frame] = st->expind[st->frame+1];
+    st->a_minimums[st->frame] = st->a_minimums[st->frame+1];
+    st->b_minimums[st->frame] = st->b_minimums[st->frame+1];
+    st->a_maximums[st->frame] = st->a_maximums[st->frame+1];
+    st->b_maximums[st->frame] = st->b_maximums[st->frame+1];
+  }
+  st->maxframe--;
+  go_back(st);
+}
+
+static void
+InitBuffer(struct state *st)
+{
+  int i;
+
+  for (i = 0 ; i < st->maxcolor; ++i)
+    st->Points.npoints[i] = 0;
+}
+
+static void
+BufferPoint(struct state *st, int color, int x, int y)
+{
+  if (st->maxcolor > MAXCOLOR)
+    abort();
+
+  /* Guard against bogus color values. Shouldn't be necessary but paranoia
+     is good. */
+  if (color < 0)
+    color = 0;
+  else if (color >= st->maxcolor)
+    color = st->maxcolor - 1;
+
+  if (st->Points.npoints[color] == MAXPOINTS)
+    {
+      XDrawPoints(st->dpy, st->canvas, st->Data_GC[color],
+                  st->Points.data[color], st->Points.npoints[color], 
+                  CoordModeOrigin);
+#ifdef BACKING_PIXMAP
+      XDrawPoints(st->dpy, st->pixmap, st->Data_GC[color],
+                  st->Points.data[color], st->Points.npoints[color], 
+                  CoordModeOrigin);
+#endif
+      st->Points.npoints[color] = 0;
+    }
+  st->Points.data[color][st->Points.npoints[color]].x = x;
+  st->Points.data[color][st->Points.npoints[color]].y = y;
+  ++st->Points.npoints[color];
+}
+
+static void
+FlushBuffer(struct state *st)
+{
+  int color;
+
+  for (color = 0; color < st->maxcolor; ++color)
+    if (st->Points.npoints[color])
+      {
+        XDrawPoints(st->dpy, st->canvas, st->Data_GC[color],
+                    st->Points.data[color], st->Points.npoints[color],
+                    CoordModeOrigin);
+#ifdef BACKING_PIXMAP
+        XDrawPoints(st->dpy, st->pixmap, st->Data_GC[color],
+                    st->Points.data[color], st->Points.npoints[color],
+                    CoordModeOrigin);
+#endif
+        st->Points.npoints[color] = 0;
+      }
+}
+
+static void
+print_help(struct state *st)
+{
+  printf("During run-time, interactive control can be exerted via : \n");
+  printf("Mouse buttons allow rubber-banding of a zoom box\n");
+  printf("< halves the 'dwell', > doubles the 'dwell'\n");
+  printf("[ halves the 'settle', ] doubles the 'settle'\n");
+  printf("D flushes the drawing buffer\n");
+  printf("e or E recalculates color indices\n");
+  printf("f or F saves exponents to a file\n");
+  printf("h or H or ? displays this message\n");
+  printf("i decrements, I increments the stripe interval\n");
+  printf("KJMN increase/decrease minimum negative exponent\n");
+  printf("m increments the map index, changing maps\n");
+  printf("p or P reverses the colormap for negative/positive exponents\n");
+  printf("r redraws without recalculating\n");
+  printf("R redraws, recalculating with new dwell and settle values\n");
+  printf("s or S spins the colorwheel\n");
+  printf("u pops back up to the last zoom\n");
+  printf("U pops back up to the first picture\n");
+  printf("v or V displays the values of various settings\n");
+  printf("w decrements, W increments the color wheel index\n");
+  printf("x or X clears the window\n");
+  printf("q or Q exits\n");
+}
+
+static void
+print_values(struct state *st)
+{
+  int i;
+  printf("\nminlyap=%f minexp=%f maxexp=%f\n",
+         st->minlyap,st->minexp, st->maxexp);
+  printf("width=%d height=%d\n",st->width,st->height);
+  printf("settle=%d  dwell=%d st->start_x=%f\n",
+         st->settle,st->dwell, st->start_x);
+  printf("min_a=%f  a_rng=%f        max_a=%f\n",
+         st->min_a,st->a_range,st->max_a);
+  printf("min_b=%f  b_rng=%f        max_b=%f\n",
+         st->min_b,st->b_range,st->max_b);
+  if (st->Rflag)
+    printf("pseudo-random forcing\n");
+  else if (st->force) {
+    printf("periodic forcing=");
+    for (i=0;i<st->maxindex;i++)
+      printf("%d",st->forcing[i]);
+    printf("\n");
+  }
+  else
+    printf("periodic forcing=01\n");
+  if (st->Force) {
+    printf("function forcing=");
+    for (i=0;i<st->funcmaxindex;i++) {
+      printf("%d",st->Forcing[i]);
+    }
+    printf("\n");
+  }
+  printf("numcolors=%d\n",st->numcolors-1);
+}
+
+static void
+freemem(struct state *st)
+{
+  int i;
+  for (i=0;i<MAXFRAMES;i++)
+    free(st->exponents[i]);
+}
+
+static void
+setupmem(struct state *st)
+{
+  int i;
+  for (i=0;i<MAXFRAMES;i++) {
+    if((st->exponents[i]=
+        (double *)malloc(sizeof(double)*st->width*(st->height+1)))==NULL){
+      fprintf(stderr,"Error malloc'ing exponent array.\n");
+      exit(-1);
+    }
+  }
+}
+
+static void
+setforcing(struct state *st)
+{
+  int i;
+  for (i=0;i<MAXINDEX;i++)
+    st->forcing[i] = (random() > st->prob) ? 0 : 1;
+}
+
+/****************************************************************************/
+
+static void
+do_defaults (struct state *st)
+{
+  int i;
+
+  memset (st->expind,  0, sizeof(st->expind));
+  memset (st->resized, 0, sizeof(st->resized));
+
+  st->aflag = 0;
+  st->bflag = 0;
+  st->hflag = 0;
+  st->wflag = 0;
+  st->minexp = 0;
+  st->mapindex = 0;
+
+# ifdef SIXTEEN_COLORS
+  st->maxcolor=16;
+  st->startcolor=0;
+  st->color_offset=0;
+  st->mincolindex=1;
+  st->dwell=50;
+  st->settle=25;
+  st->xposition=128;
+  st->yposition=128;
+# else  /* !SIXTEEN_COLORS */
+  st->maxcolor=256;
+  st->startcolor=17;
+  st->color_offset=96;
+  st->mincolindex=33;
+  st->dwell=100;
+  st->settle=50;
+# endif /* !SIXTEEN_COLORS */
+
+  st->maxindex = MAXINDEX;
+  st->funcmaxindex = FUNCMAXINDEX;
+  st->min_a=2.0;
+  st->min_b=2.0;
+  st->a_range=2.0;
+  st->b_range=2.0;
+  st->minlyap=1.0;
+  st->max_a=4.0;
+  st->max_b=4.0;
+  st->numcolors=16;
+  st->prob=0.5;
+  st->numwheels=MAXWHEELS;
+  st->negative=1;
+  st->rgb_max=65000;
+  st->nostart=1;
+  st->stripe_interval=7;
+  st->save=1;
+  st->useprod=1;
+  st->spinlength=256;
+  st->run=1;
+
+  for (i = 0; i < countof(st->forcing); i++)
+    st->forcing[i] = (i & 1) ? 1 : 0;
+}
+
+static void
+do_preset (struct state *st, int builtin)
+{
+  char *ff = 0;
+  switch (builtin) {
+  case 0:
+    st->min_a = 3.75; st->aflag++;
+    st->min_b = 3.299999; st->bflag++;
+    st->a_range = 0.05; st->wflag++;
+    st->b_range = 0.05; st->hflag++;
+    st->dwell = 200;
+    st->settle = 100;
+    ff = "abaabbaaabbb";
+    break;
+
+  case 1:
+    st->min_a = 3.8; st->aflag++;
+    st->min_b = 3.2; st->bflag++;
+    st->b_range = .05; st->hflag++;
+    st->a_range = .05; st->wflag++;
+    ff = "bbbbbaaaaa";
+    break;
+
+  case 2:
+    st->min_a =  3.4; st->aflag++;
+    st->min_b =  3.04; st->bflag++;
+    st->a_range =  .5; st->wflag++;
+    st->b_range =  .5; st->hflag++;
+    ff = "abbbbbbbbb";
+    st->settle = 500;
+    st->dwell = 1000;
+    break;
+
+  case 3:
+    st->min_a = 3.5; st->aflag++;
+    st->min_b = 3.0; st->bflag++;
+    st->a_range = 0.2; st->wflag++;
+    st->b_range = 0.2; st->hflag++;
+    st->dwell = 600;
+    st->settle = 300;
+    ff = "aaabbbab";
+    break;
+
+  case 4:
+    st->min_a = 3.55667; st->aflag++;
+    st->min_b = 3.2; st->bflag++;
+    st->b_range = .05; st->hflag++;
+    st->a_range = .05; st->wflag++;
+    ff = "bbbbbaaaaa";
+    break;
+
+  case 5:
+    st->min_a = 3.79; st->aflag++;
+    st->min_b = 3.22; st->bflag++;
+    st->b_range = .02999; st->hflag++;
+    st->a_range = .02999; st->wflag++;
+    ff = "bbbbbaaaaa";
+    break;
+
+  case 6:
+    st->min_a = 3.7999; st->aflag++;
+    st->min_b = 3.299999; st->bflag++;
+    st->a_range = 0.2; st->wflag++;
+    st->b_range = 0.2; st->hflag++;
+    st->dwell = 300;
+    st->settle = 150;
+    ff = "abaabbaaabbb";
+    break;
+
+  case 7:
+    st->min_a = 3.89; st->aflag++;
+    st->min_b = 3.22; st->bflag++;
+    st->b_range = .028; st->hflag++;
+    st->a_range = .02999; st->wflag++;
+    ff = "bbbbbaaaaa";
+    st->settle = 600;
+    st->dwell = 1000;
+    break;
+
+  case 8:
+    st->min_a = 3.2; st->aflag++;
+    st->min_b = 3.7; st->bflag++;
+    st->a_range = 0.05; st->wflag++;
+    st->b_range = .005; st->hflag++;
+    ff = "abbbbaa";
+    break;
+
+  case 9:
+    ff = "aaaaaabbbbbb";
+    st->mapindex = 1;
+    st->dwell =  400;
+    st->settle =  200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  case 10:
+    ff = "aaaaaabbbbbb";
+    st->mapindex = 1;
+    st->dwell =  400;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  case 11:
+    st->mapindex = 1;
+    st->dwell =  400;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  case 12:
+    ff = "abbb";
+    st->mapindex = 1;
+    st->dwell =  400;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  case 13:
+    ff = "abbabaab";
+    st->mapindex = 1;
+    st->dwell =  400;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  case 14:
+    ff = "abbabaab";
+    st->dwell =  800;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    /* ####  -x 0.05 */
+    st->min_a = 3.91; st->aflag++;
+    st->a_range =  0.0899999999; st->wflag++;
+    st->min_b =  3.28; st->bflag++;
+    st->b_range =  0.35; st->hflag++;
+    break;
+
+  case 15:
+    ff = "aaaaaabbbbbb";
+    st->dwell =  400;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  case 16:
+    st->dwell =  400;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  case 17:
+    ff = "abbb";
+    st->dwell =  400;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  case 18:
+    ff = "abbabaab";
+    st->dwell =  400;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  case 19:
+    st->mapindex = 2;
+    ff = "aaaaaabbbbbb";
+    st->dwell =  400;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  case 20:
+    st->mapindex = 2;
+    st->dwell =  400;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  case 21:
+    st->mapindex = 2;
+    ff = "abbb";
+    st->dwell =  400;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  case 22:
+    st->mapindex = 2;
+    ff = "abbabaab";
+    st->dwell =  400;
+    st->settle = 200;
+    st->minlyap = st->maxexp = ABS(-0.85);
+    st->minexp = -1.0 * st->minlyap;
+    break;
+
+  default: 
+    abort();
+    break;
+  }
+
+  if (ff) {
+    char *ch;
+    int bindex = 0;
+    st->maxindex = strlen(ff);
+    if (st->maxindex > MAXINDEX)
+      usage(st);
+    ch = ff;
+    st->force++;
+    while (bindex < st->maxindex) {
+      if (*ch == 'a')
+        st->forcing[bindex++] = 0;
+      else if (*ch == 'b')
+        st->forcing[bindex++] = 1;
+      else
+        usage(st);
+      ch++;
+    }
+  }
+}
+
+
+static void *
+xlyap_init (Display *d, Window window)
+{
+  struct state *st = (struct state *) calloc (1, sizeof(*st));
+  XWindowAttributes xgwa;
+  int builtin = -1;
+  XGetWindowAttributes (d, window, &xgwa);
+  st->dpy = d;
+  st->width = xgwa.width;
+  st->height = xgwa.height;
+  st->visual = xgwa.visual;
+  st->screen = xgwa.screen;
+  st->cmap = xgwa.colormap;
+
+  do_defaults(st);
+  parseargs(st);
+
+  if (get_boolean_resource(st->dpy, "randomize", "Boolean"))
+    builtin = random() % NBUILTINS;
+  else {
+    char *s = get_string_resource(st->dpy, "builtin", "Integer");
+    if (s && *s)
+      builtin = atoi(s);
+    if (s) free (s);
+  }
+    
+  if (builtin >= 0)
+    do_preset (st, builtin);
+
+  st->background = BlackPixelOfScreen(st->screen);
+  setupmem(st);
+  init_data(st);
+  if (!mono_p)
+    st->foreground = st->startcolor;
+  else
+    st->foreground = WhitePixelOfScreen(st->screen);
+
+  /*
+   * Create the window to display the Lyapunov exponents
+   */
+  st->canvas = window;
+  init_color(st);
+
+#ifdef BACKING_PIXMAP
+  st->pixmap = XCreatePixmap(st->dpy, window, st->width, st->height, 
+                             xgwa.depth);
+#endif
+/*  st->rubber_data.band_cursor = XCreateFontCursor(st->dpy, XC_hand2);*/
+/*  CreateXorGC(st);*/
+  Clear(st);
+
+  st->delay  = get_integer_resource(st->dpy, "delay", "Delay");
+  st->linger = get_integer_resource(st->dpy, "linger", "Linger");
+  if (st->linger < 1) st->linger = 1;
+
+  return st;
+}
+
+
+static unsigned long
+xlyap_draw (Display *dpy, Window window, void *closure)
+{
+  struct state *st = (struct state *) closure;
+  int i;
+
+  if (!st->run && st->reset_countdown) {
+    st->reset_countdown--;
+    if (st->reset_countdown)
+      return 1000000;
+    else {
+      do_defaults (st);
+      do_preset (st, (random() % NBUILTINS));
+      Clear (st);
+      init_data(st);
+      init_color(st);
+      resize (st);
+      st->frame = 0;
+      st->run = 1;
+    }
+  }
+
+  for (i = 0; i < 1000; i++)
+    if (complyap(st) == TRUE)
+      {
+        st->run = 0;
+        st->reset_countdown = st->linger;
+        break;
+      }
+  return st->delay;
+}
+
+static void
+xlyap_reshape (Display *dpy, Window window, void *closure, 
+                 unsigned int w, unsigned int h)
+{
+  struct state *st = (struct state *) closure;
+  resize(st);
+}
+
+static Bool
+xlyap_event (Display *dpy, Window window, void *closure, XEvent *event)
+{
+  struct state *st = (struct state *) closure;
+
+  switch(event->type)
+    {
+    case KeyPress:
+      if (Getkey(st, &event->xkey))
+        return True;
+      break;
+#if 0
+    case ButtonPress:
+      StartRubberBand(st, &st->rubber_data, event);
+      return True;
+    case MotionNotify:
+      TrackRubberBand(st, &st->rubber_data, event);
+      return True;
+    case ButtonRelease:
+      EndRubberBand(st, &st->rubber_data, event);
+      return True;
+#endif
+    default: 
+      break;
+    }
+
+  if (screenhack_event_helper (dpy, window, event))
+    {
+      Clear(st);
+      return True;
+    }
+
+  return False;
+}
+
+static void
+xlyap_free (Display *dpy, Window window, void *closure)
+{
+  int i;
+  struct state *st = (struct state *) closure;
+
+  freemem (st);
+
+#ifdef BACKING_PIXMAP
+  XFreePixmap (st->dpy, st->pixmap);
+#endif
+/*  XFreeGC (st->dpy, st->RubberGC);*/
+  for (i = 0; i < st->maxcolor; i++)
+    XFreeGC (st->dpy, st->Data_GC[i]);
+
+  free (st);
+}
+
+
+XSCREENSAVER_MODULE ("XLyap", xlyap)