Fractal Mandelbrot With Arduino

1//mandelbrot06.ino
2// http://rosettacode.org/wiki/Mandelbrot_set
3//  https://www.khanacademy.org/computer-programming/mandelbrot-set/1054272371
4//  https://github.com/cslarsen/mandelbrot-js
5// http://falcosoft.hu/html5_mandelbrot.html
6//
7int  pinOnBoardLED = 13;
8long startTime = 0;
9
10void setup() {
11  Serial.begin(9600);
12  pinMode(pinOnBoardLED, OUTPUT);
13}
14
15void loop() {
16  myMandel(-2.000,  1.000, -1.000,  1.000, 99, 50, 140);
17  myMandel(-2.0262812499999998, -1.7157656249999997,  0.1242708333333333, -0.1088020833333334, 99, 50, 140);
18  myMandel(0.3086785098726753,  0.5163214901273253, -0.2804711524861787, -0.4345288475138219, 150, 50, 140);
19  myMandel(0.4329398558688174, 0.4498108480145078, -0.3687333735957660, -0.3812505613167620,  200, 50, 140);
20  myMandel(0.4357822854352487, 0.4359042777391612, -0.3780553779480240,  -0.3781461752993666, 250, 50, 140);
21}
22
23void switchLED() {
24  digitalWrite(pinOnBoardLED,  digitalRead(pinOnBoardLED) ^ 1);
25}
26
27void myMandel(double realMin, double  realMax, double imagMin, double imagMax, int maxIterations, double ySize, double  xSize) {
28  // http://rosettacode.org/wiki/Mandelbrot_set#AWK
29  startTime =  millis();
30  String myString = "\
31\
32\
33\
34realMin=" + String(realMin) + ",  realMax=" + String(realMax) + ", imagMin=" + String(imagMin) + ", imagMax="  + String(imagMax) + ", maxIterations=" + String(maxIterations) + ", startTime="  + String((startTime / 1000.0)) + "s";
35  Serial.print(myString);
36  //================================================================
37  double xStep = (realMax - realMin) / xSize;
38  double yStep = (imagMax - imagMin)  / ySize;
39  char* colorChar[] = {"#", "-", ":", "=", "o"};
40  int  colorCharLength = (sizeof(colorChar) / sizeof(colorChar[0])) - 1;
41  int color  = 0;
42  for (int y = 0; y < ySize; y++) {
43    Serial.print("\
44");
45    switchLED();
46    double imagY = imagMin + yStep * y;
47    for (int x = 0; x < xSize; x++) {
48      double realX = realMin + xStep * x;
49      double realZ = realX;
50      double  imagZ = imagY;
51      for (int n = 0; n <= maxIterations; n++) {
52        color  = n;
53        double a = realZ * realZ;
54        double b = imagZ * imagZ;
55        if (a + b > 4.0) break;
56        imagZ = 2 * realZ * imagZ + imagY;
57        realZ = a - b + realX;
58      }
59      (color == maxIterations ) ? color  = 0 : color = color % colorCharLength + 1;
60      Serial.print(colorChar[color]);
61    }
62  }
63  //================================================================
64  long elapseTime = millis() - startTime;
65  myString = "\
66elapseTime=" + String((elapseTime  / 1000.0)) + "s";
67  Serial.print(myString);
68}