Been playing with some code for generating symmetric chaos, from the book by Michael Field and Martin Golubitsky – Symmetry in Chaos.

Just a wee bit of processing, it uses the ControlP5 lib for value sliders.

Anyway here it is.

import processing.opengl.*;
import controlP5.*;
ControlP5 controlP5;
MyControlListener myListener;
int iter = 1000;
float lambda = -2.54;
float alph = 5.0;
float beta = -2.0;
float gamma = 1.05;
float omega = 0.19;
int degree = 6;
int scaling = 40;
int ss = 600;
boolean stop = false;
float x = 0.01; float y = 0.003;
int cols [][] = new int[ss][ss];
void setup() {
size(ss, ss, OPENGL);
smooth();
resetPixels();
// sliders
controlP5 = new ControlP5(this);
controlP5.addSlider("lambda", -4, 4, lambda, 10, 10, 500, 10);
controlP5.addSlider("alph", -10, 10, alph, 10, 30, 500, 10);
controlP5.addSlider("beta", -20, 20, beta, 10, 50, 500, 10);
controlP5.addSlider("gamma", -4, 4, gamma, 10, 70, 500, 10);
controlP5.addSlider("omega", -4, 4, omega, 10, 90, 500, 10);
controlP5.addSlider("scaling", 0, 200, scaling, 10, 110, 100, 10);
controlP5.addSlider("degree", 3, 40, degree, 10, 130, 100, 10);
myListener = new MyControlListener();
controlP5.controller("lambda").addListener(myListener);
controlP5.controller("alph").addListener(myListener);
controlP5.controller("beta").addListener(myListener);
controlP5.controller("gamma").addListener(myListener);
controlP5.controller("omega").addListener(myListener);
controlP5.controller("scaling").addListener(myListener);
controlP5.controller("degree").addListener(myListener);
background(0);
colorMode(HSB, 360, 100, 100, 1);
}
void draw() {
for(int j = 0; j < iter; j++) {
float zzbar = x*x + y*y;
float zreal = x;
float zimag = y;
for(int i = 0; i < degree - 2; i++) {
float za = zreal*x - zimag*y;
float zb = zimag*x + zreal*y;
zreal = za;
zimag = zb;
}
float zn = x*zreal - y*zimag;
loat p = lambda + alph*zzbar + beta*zn;
float xnew = p*x + gamma*zreal - omega*y;
float ynew = p*y - gamma*zimag + omega*x;
int xi = (int)(xnew*(ss/2 - scaling)+ss/2);
int yi = (int)(ynew*(ss/2 - scaling)+ss/2);
if(xi >= 0 && xi < ss && yi >= 0 && yi < ss0) {
cols[xi][yi]++;
stroke(360-cols[xi][yi], 70, 70, 0.7);
point(xnew*(ss/2 - scaling)+ss/2, ynew*(ss/2 - scaling)+ss/2);
x = xnew; y = ynew;
}
}
}
void resetPixels() {
for(int i = 0; i < ss; i++) {
for(int j = 0; j < ss; j++) {
cols[i][j] = 0;
}
}
}
class MyControlListener implements ControlListener {
public void controlEvent(ControlEvent theEvent) {
background(0);
x = 0.01; y = 0.003;
resetPixels();
}
}

The initial image is a nice 6 fold pattern, that looks somewhat like a flower