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+/* -*- Mode: C; tab-width: 4 -*- */
+/* discrete --- chaotic mappings */
+
+#if 0
+static const char sccsid[] = "@(#)discrete.c 5.00 2000/11/01 xlockmore";
+#endif
+
+/*-
+ * Copyright (c) 1996 by Tim Auckland <tda10.geo@yahoo.com>
+ *
+ * Permission to use, copy, modify, and distribute this software and its
+ * documentation for any purpose and without fee is hereby granted,
+ * provided that the above copyright notice appear in all copies and that
+ * both that copyright notice and this permission notice appear in
+ * supporting documentation.
+ *
+ * This file is provided AS IS with no warranties of any kind. The author
+ * shall have no liability with respect to the infringement of copyrights,
+ * trade secrets or any patents by this file or any part thereof. In no
+ * event will the author be liable for any lost revenue or profits or
+ * other special, indirect and consequential damages.
+ *
+ * "discrete" shows a number of fractals based on the "discrete map"
+ * type of dynamical systems. They include a different way of looking
+ * at the HOPALONG system, an inverse julia-set iteration, the "Standard
+ * Map" and the "Bird in a Thornbush" fractal.
+ *
+ * Revision History:
+ * 01-Nov-2000: Allocation checks
+ * 31-Jul-1997: Ported to xlockmore-4
+ * 08-Aug-1996: Adapted from hop.c Copyright (c) 1991 by Patrick J. Naughton.
+ */
+
+#ifdef STANDALONE
+# define MODE_discrete
+#define DEFAULTS "*delay: 20000 \n" \
+ "*count: 4096 \n" \
+ "*cycles: 2500 \n" \
+ "*ncolors: 100 \n" \
+ "*fpsSolid: true \n" \
+ "*ignoreRotation: True \n" \
+ "*lowrez: True \n" \
+
+# define SMOOTH_COLORS
+# define release_discrete 0
+# define discrete_handle_event 0
+# include "xlockmore.h" /* in xscreensaver distribution */
+#else /* STANDALONE */
+# include "xlock.h" /* in xlockmore distribution */
+#endif /* STANDALONE */
+
+#ifdef MODE_discrete
+
+ENTRYPOINT ModeSpecOpt discrete_opts =
+{0, (XrmOptionDescRec *) NULL, 0, (argtype *) NULL, (OptionStruct *) NULL};
+
+#ifdef USE_MODULES
+ModStruct discrete_description =
+{"discrete", "init_discrete", "draw_discrete", (char *) NULL,
+ "refresh_discrete", "init_discrete", "free_discrete", &discrete_opts,
+ 1000, 4096, 2500, 1, 64, 1.0, "",
+ "Shows various discrete maps", 0, NULL};
+
+#endif
+
+enum ftypes {
+ SQRT, BIRDIE, STANDARD, TRIG, CUBIC, HENON, AILUJ, HSHOE, DELOG
+};
+
+/*#define TEST STANDARD */
+
+#define BIASES 18
+static enum ftypes bias[BIASES] =
+{
+ STANDARD, STANDARD, STANDARD, STANDARD,
+ SQRT, SQRT, SQRT, SQRT,
+ BIRDIE, BIRDIE, BIRDIE,
+ AILUJ, AILUJ, AILUJ,
+ TRIG, TRIG,
+ CUBIC,
+ HENON,
+};
+
+typedef struct {
+ int maxx;
+ int maxy; /* max of the screen */
+ double a;
+ double b;
+ double c;
+ double d;
+ double e;
+ double i;
+ double j; /* discrete parameters */
+ double ic;
+ double jc;
+ double is;
+ double js;
+ int inc;
+ int pix;
+ enum ftypes op;
+ int count;
+ XPoint *pointBuffer; /* pointer for XDrawPoints */
+
+ int sqrt_sign, std_sign;
+
+} discretestruct;
+
+static discretestruct *discretes = (discretestruct *) NULL;
+
+ENTRYPOINT void
+init_discrete (ModeInfo * mi)
+{
+ double range;
+ discretestruct *hp;
+
+ MI_INIT (mi, discretes);
+ hp = &discretes[MI_SCREEN(mi)];
+
+ hp->maxx = MI_WIDTH(mi);
+ hp->maxy = MI_HEIGHT(mi);
+#ifdef TEST
+ hp->op = TEST;
+#else
+ hp->op = bias[LRAND() % BIASES];
+#endif
+ switch (hp->op) {
+ case HSHOE:
+ hp->ic = 0;
+ hp->jc = 0;
+ hp->is = hp->maxx / (4);
+ hp->js = hp->maxy / (4);
+ hp->a = 0.5;
+ hp->b = 0.5;
+ hp->c = 0.2;
+ hp->d = -1.25;
+ hp->e = 1;
+ hp->i = hp->j = 0.0;
+ break;
+ case DELOG:
+ hp->ic = 0.5;
+ hp->jc = 0.3;
+ hp->is = hp->maxx / 1.5;
+ hp->js = hp->maxy / 1.5;
+ hp->a = 2.176399;
+ hp->i = hp->j = 0.01;
+ break;
+ case HENON:
+ hp->jc = ((LRAND() / MAXRAND) * 2.0 - 1.0) * 0.4;
+ hp->ic = 1.3 * (1 - (hp->jc * hp->jc) / (0.4 * 0.4));
+ hp->is = hp->maxx;
+ hp->js = hp->maxy * 1.5;
+ hp->a = 1;
+ hp->b = 1.4;
+ hp->c = 0.3;
+ hp->i = hp->j = 0;
+ break;
+ case SQRT:
+ hp->ic = 0;
+ hp->jc = 0;
+ hp->is = 1;
+ hp->js = 1;
+ range = sqrt((double) hp->maxx * 2 * hp->maxx * 2 +
+ (double) hp->maxy * 2 * hp->maxy * 2) /
+ (10.0 + LRAND() % 10);
+
+ hp->a = (LRAND() / MAXRAND) * range - range / 2.0;
+ hp->b = (LRAND() / MAXRAND) * range - range / 2.0;
+ hp->c = (LRAND() / MAXRAND) * range - range / 2.0;
+ if (!(LRAND() % 2))
+ hp->c = 0.0;
+ hp->i = hp->j = 0.0;
+ break;
+ case STANDARD:
+ hp->ic = M_PI;
+ hp->jc = M_PI;
+ hp->is = hp->maxx / (M_PI * 2);
+ hp->js = hp->maxy / (M_PI * 2);
+ hp->a = 0; /* decay */
+ hp->b = (LRAND() / MAXRAND) * 2.0;
+ hp->c = 0;
+ hp->i = M_PI;
+ hp->j = M_PI;
+ break;
+ case BIRDIE:
+ hp->ic = 0;
+ hp->jc = 0;
+ hp->is = hp->maxx / 2;
+ hp->js = hp->maxy / 2;
+ hp->a = 1.99 + ((LRAND() / MAXRAND) * 2.0 - 1.0) * 0.2;
+ hp->b = 0;
+ hp->c = 0.8 + ((LRAND() / MAXRAND) * 2.0 - 1.0) * 0.1;
+ hp->i = hp->j = 0;
+ break;
+ case TRIG:
+ hp->a = 5;
+ hp->b = 0.5 + ((LRAND() / MAXRAND) * 2.0 - 1.0) * 0.3;
+ hp->ic = hp->a;
+ hp->jc = 0;
+ hp->is = hp->maxx / (hp->b * 20);
+ hp->js = hp->maxy / (hp->b * 20);
+ hp->i = hp->j = 0;
+ break;
+ case CUBIC:
+ hp->a = 2.77;
+ hp->b = 0.1 + ((LRAND() / MAXRAND) * 2.0 - 1.0) * 0.1;
+ hp->ic = 0;
+ hp->jc = 0;
+ hp->is = hp->maxx / 4;
+ hp->js = hp->maxy / 4;
+ hp->i = hp->j = 0.1;
+ break;
+ case AILUJ:
+ {
+ int i;
+ double x, y, xn, yn;
+
+ hp->ic = 0;
+ hp->jc = 0;
+ hp->is = hp->maxx / 4;
+ hp->js = hp->maxx / 4;
+ do {
+ hp->a = ((LRAND() / MAXRAND) * 2.0 - 1.0) * 1.5 - 0.5;
+ hp->b = ((LRAND() / MAXRAND) * 2.0 - 1.0) * 1.5;
+ x = y = 0;
+#define MAXITER 10
+ for (i = 0; i < MAXITER && x * x + y * y < 13; i++) { /* 'Brot calc */
+ xn = x * x - y * y + hp->a;
+ yn = 2 * x * y + hp->b;
+ x = xn;
+ y = yn;
+ }
+ } while (i < MAXITER); /* wait for a connected set */
+ hp->i = hp->j = 0.1;
+ break;
+ }
+ }
+ hp->pix = 0;
+ hp->inc = 0;
+
+ if (hp->pointBuffer == NULL) {
+ hp->pointBuffer = (XPoint *) malloc(sizeof (XPoint) * MI_COUNT(mi));
+ /* if fails will check later */
+ }
+
+ /* Clear the background. */
+ MI_CLEARWINDOW(mi);
+
+ XSetForeground(MI_DISPLAY(mi), MI_GC(mi), MI_WHITE_PIXEL(mi));
+ hp->count = 0;
+ hp->sqrt_sign = 1;
+ hp->std_sign = 1;
+}
+
+
+static void
+draw_discrete_1 (ModeInfo * mi)
+{
+ Display *dsp = MI_DISPLAY(mi);
+ Window win = MI_WINDOW(mi);
+ double oldj, oldi;
+ int count = MI_COUNT(mi);
+ int cycles = MI_CYCLES(mi);
+ int k;
+ XPoint *xp;
+ GC gc = MI_GC(mi);
+ discretestruct *hp;
+
+ if (discretes == NULL)
+ return;
+ hp = &discretes[MI_SCREEN(mi)];
+ if (hp->pointBuffer == NULL)
+ return;
+
+ k = count;
+ xp = hp->pointBuffer;
+
+ hp->inc++;
+
+ MI_IS_DRAWN(mi) = True;
+
+ if (MI_NPIXELS(mi) > 2) {
+ XSetForeground(dsp, gc, MI_PIXEL(mi, hp->pix));
+ if (++hp->pix >= MI_NPIXELS(mi))
+ hp->pix = 0;
+ }
+ while (k--) {
+ oldj = hp->j;
+ oldi = hp->i;
+ switch (hp->op) {
+ case HSHOE:
+ {
+ int i;
+
+#if 0
+ if (!k) {
+ XSetForeground(dsp, gc, MI_BLACK_PIXEL(mi));
+ XFillRectangle(dsp, win, gc, 0, 0, hp->maxx, hp->maxy);
+ XSetForeground(dsp, gc, MI_PIXEL(mi, hp->pix));
+ } else
+#endif
+#define HD
+#ifdef HD
+ if (k < count / 4) {
+ hp->i = ((double) k / count) * 8 - 1;
+ hp->j = 1;
+ } else if (k < count / 2) {
+ hp->i = 1;
+ hp->j = 3 - ((double) k / count) * 8;
+ } else if (k < 3 * count / 4) {
+ hp->i = 5 - ((double) k / count) * 8;
+ hp->j = -1;
+ } else {
+ hp->i = -1;
+ hp->j = ((double) k / count) * 8 - 7;
+ }
+ for (i = 1; i < (hp->inc % 15); i++) {
+ oldj = hp->j;
+ oldi = hp->i;
+#endif
+ hp->i = (hp->a * oldi + hp->b) * oldj;
+ hp->j = (hp->e - hp->d + hp->c * oldi) * oldj * oldj - hp->c * oldi + hp->d;
+#ifdef HD
+ }
+#endif
+ break;
+ }
+ case DELOG:
+ hp->j = oldi;
+ hp->i = hp->a * oldi * (1 - oldj);
+ break;
+ case HENON:
+ hp->i = oldj + hp->a - hp->b * oldi * oldi;
+ hp->j = hp->c * oldi;
+ break;
+ case SQRT:
+ if (k) {
+ hp->j = hp->a + hp->i;
+ hp->i = -oldj + (hp->i < 0
+ ? sqrt(fabs(hp->b * (hp->i - hp->c)))
+ : -sqrt(fabs(hp->b * (hp->i - hp->c))));
+ } else {
+ hp->i = (hp->sqrt_sign ? 1 : -1) * hp->inc * hp->maxx / cycles / 2;
+ hp->j = hp->a + hp->i;
+ hp->sqrt_sign = !hp->sqrt_sign;
+ }
+ break;
+ case STANDARD:
+ if (k) {
+ hp->j = (1 - hp->a) * oldj + hp->b * sin(oldi) + hp->a * hp->c;
+ hp->j = fmod(hp->j + 2 * M_PI, 2 * M_PI);
+ hp->i = oldi + hp->j;
+ hp->i = fmod(hp->i + 2 * M_PI, 2 * M_PI);
+ } else {
+ hp->j = M_PI + fmod((hp->std_sign ? 1 : -1) * hp->inc * 2 * M_PI / (cycles - 0.5), M_PI);
+ hp->i = M_PI;
+ hp->std_sign = !hp->std_sign;
+ }
+ break;
+ case BIRDIE:
+ hp->j = oldi;
+ hp->i = (1 - hp->c) * cos(M_PI * hp->a * oldj) + hp->c * hp->b;
+ hp->b = oldj;
+ break;
+ case TRIG:
+ {
+ double r2 = oldi * oldi + oldj * oldj;
+
+ hp->i = hp->a + hp->b * (oldi * cos(r2) - oldj * sin(r2));
+ hp->j = hp->b * (oldj * cos(r2) + oldi * sin(r2));
+ }
+ break;
+ case CUBIC:
+ hp->i = oldj;
+ hp->j = hp->a * oldj - oldj * oldj * oldj - hp->b * oldi;
+ break;
+ case AILUJ:
+ hp->i = ((LRAND() < MAXRAND / 2) ? -1 : 1) *
+ sqrt(((oldi - hp->a) +
+ sqrt((oldi - hp->a) * (oldi - hp->a) + (oldj - hp->b) * (oldj - hp->b))) / 2);
+ if (hp->i < 0.00000001 && hp->i > -0.00000001)
+ hp->i = (hp->i > 0.0) ? 0.00000001 : -0.00000001;
+ hp->j = (oldj - hp->b) / (2 * hp->i);
+ break;
+ }
+ xp->x = hp->maxx / 2 + (int) ((hp->i - hp->ic) * hp->is);
+ xp->y = hp->maxy / 2 - (int) ((hp->j - hp->jc) * hp->js);
+ xp++;
+ }
+ XDrawPoints(dsp, win, gc, hp->pointBuffer, count, CoordModeOrigin);
+}
+
+ENTRYPOINT void
+draw_discrete (ModeInfo * mi)
+{
+ discretestruct *hp = &discretes[MI_SCREEN(mi)];
+ int cycles = MI_CYCLES(mi);
+ int i;
+
+ for (i = 0; i < 10; i++) {
+ draw_discrete_1 (mi);
+ hp->count++;
+ }
+
+ if (hp->count > cycles) {
+ init_discrete(mi);
+ }
+}
+
+
+ENTRYPOINT void
+reshape_discrete(ModeInfo * mi, int width, int height)
+{
+ discretestruct *hp = &discretes[MI_SCREEN(mi)];
+ hp->maxx = width;
+ hp->maxy = height;
+ XClearWindow (MI_DISPLAY (mi), MI_WINDOW(mi));
+}
+
+ENTRYPOINT void
+free_discrete(ModeInfo * mi)
+{
+ discretestruct *hp = &discretes[MI_SCREEN(mi)];
+
+ if (hp->pointBuffer != NULL) {
+ (void) free((void *) hp->pointBuffer);
+ /* hp->pointBuffer = NULL; */
+ }
+}
+
+#ifndef STANDALONE
+ENTRYPOINT void
+refresh_discrete(ModeInfo * mi)
+{
+ MI_CLEARWINDOW(mi);
+}
+#endif
+
+XSCREENSAVER_MODULE ("Discrete", discrete)
+
+#endif /* MODE_discrete */
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