Fractal generation from infinite sum - graphics

Question

I found a project description on a course website for computer graphics. I am trying to complete the project for fun.
Here is the link to the problem description:
http://www.pdfhost.net/index.php?Action=Download&File=901bc7785bef41364b3a40f6f4493926
Below is my code. The problem I am running in to is that the terms of the series grow so fast I can't map the points to the screen correctly. From the problem description it says the points will be mappable within a -2 - 2 square but the difference in value between the points is so huge that normalizing by the largest would collapse most of the points to a single pixel.
I assume I have a fundamental misunderstanding that I can't identify. Any help or insight would be appreciated!
int w = 800, h = 600;
int numTimes = 10, cSize = 5;
float xr = 2, yr = 2;
void setup() {
size(w,h);
}
void draw() {
background(255);
Complex v = new Complex(mouseX*(xr/w) - (xr/2), mouseY*(yr/h) - (yr/2));
Complex[] exps = new Complex[numTimes];
for (int i = 0; i < numTimes; i++) {
exps[i] = complexExp(v,i);
}
ellipse(w/2, h/2, cSize, cSize);
for (int i = 0; i < numTimes; i++) {
drawSeries(new Complex(0,0), exps, i, i);
}
}
void drawSeries(Complex vToDraw, Complex[] exps, int count, int clrTrunc) {
if (count == 0) {
Complex v = exps[0];
float progress = float(clrTrunc) / float(numTimes);
fill(255*progress, 180, 255 - 255*progress);
vToDraw.add(v);
ellipse(vToDraw.r*(w/xr) + (w/2), vToDraw.i*(h/xr) + h/2, cSize, cSize);
vToDraw.sub(v);
vToDraw.sub(v);
ellipse(vToDraw.r*(w/xr) + (w/2), vToDraw.i*(h/xr) + h/2, cSize, cSize);
} else {
Complex v = exps[count];
vToDraw.add(v);
drawSeries(vToDraw, exps, count - 1, clrTrunc );
vToDraw.sub(v);
vToDraw.sub(v);
drawSeries(vToDraw, exps, count - 1,clrTrunc );
}
}
Complex complexExp(Complex v, int times) {
if (times == 0) {
return new Complex(1, 1);
} else if ( times == 1) {
return new Complex( v.r*v.r - v.i*v.i, 2*v.r*v.i );
} else {
return complexExp( new Complex( v.r*v.r - v.i*v.i, 2*v.r*v.i ), times - 1 );
}
}
class Complex {
float r, i;
Complex() {
this.r = 0;
this.i = 0;
}
Complex(float r, float i) {
this.r = r;
this.i = i;
}
void add(Complex nv) {
this.r += nv.r;
this.i += nv.i;
}
void sub(Complex nv) {
this.r -= nv.r;
this.i -= nv.i;
}
}

Answer 1

I think you can make the code cleaner if you write a more complete Complex class.
int w = 800, h = 600;
int numTimes = 10, cSize = 5;
float xr = 3, yr = 3;
void setup() {
size(w,h);
noLoop();
}
void mousePressed() {
redraw();
}
void draw() {
background(255);
Complex v = new Complex(mouseX*(xr/w) - (xr/2), mouseY*(yr/h) - (yr/2));
Complex[] exps = new Complex[numTimes];
for (int i = 0; i < numTimes; i++) {
exps[i] = v.raisedTo(i);
print(exps[i]);
}
ellipse(w/2, h/2, cSize, cSize);
print(exps);
drawSerie(exps, numTimes);
}
void drawSerie(Complex[] exps, int total)
{
Complex partial = new Complex(0, 0);
drawPartial(exps, total -1, partial);
}
void drawFinal(Complex toDraw)
{
point(toDraw.r*(w/xr) + (w/2), toDraw.i*(h/xr) + h/2);
}
void drawPartial(Complex [] exps, int depth, Complex partial)
{
if (depth == -1)
{
drawFinal(partial);
return;
}
int nextDepth = depth -1;
drawPartial(exps, nextDepth, partial);
Complex element = exps[depth];
drawPartial(exps, nextDepth, partial.add(element));
drawPartial(exps, nextDepth, partial.sub(element));
}
class Complex {
float r, i;
Complex() {
this.r = 0;
this.i = 0;
}
Complex(float r, float i) {
this.r = r;
this.i = i;
}
Complex(Complex other)
{
this.r = other.r;
this.i = other.i;
}
Complex mult(Complex other)
{
return new Complex(this.r*other.r - this.i*other.i, this.r*other.i + this.i*other.r);
}
Complex add(Complex nv) {
return new Complex(this.r + nv.r, this.i + nv.i);
}
Complex sub(Complex nv) {
return new Complex(this.r - nv.r, this.i - nv.i);
}
Complex raisedTo(int n) {
if (n == 0) {
return new Complex(1, 0);
}
else if (n % 2 == 0)
{
return (this.mult(this)).raisedTo(n/2);
}
else
{
return this.mult(this.raisedTo(n - 1 ));
}
}
String toString()
{
return "real: " + this.r + " imaginary: " + this.i;
}
}
The computation of the series is not efficient but, I think, it is clear