//Java version of Julia Set from Math Adventures with Python

//Declare 2-element array, assign to variable c
float[] c = new float[2];

//set the range of x-values
int xmin=-2;
int xmax=2;

//range of y-values
int ymin = -2;
int ymax = 2;

//calculate the range
float rangex = xmax - xmin;
float rangey = ymax - ymin;

//Declare xscl and yxscl
// We'll assign them values in setup

float xscl = rangex/600;
float yscl = rangey/600;

void setup(){
 size(600,600);
 colorMode(HSB);
 noStroke();

}
 
void draw(){
 //Declare the components of c
 c[0] = 0.25*mouseX*xscl; //real
 c[1] = 0.25*mouseY*yscl; //imaginary
 //go over all x's and y's on the grid
 for (int x=0;x<width;x++){
 for (int y=0;y<height;y++){
 float[] z ={xmin+x*xscl,ymin+y*yscl};
 //put z into the julia function
 int col=julia(z,100);
 //if julia returns 100
 //that location never diverged
 //not in julia set --> black
 if (col == 100){
 fill(0); //black
 }else{
 //calculate color from "col"
 int c1 = (255-2*col);
 fill(c1,255,255);
 }
 rect(x,y,1,1); //draw the tiny rectangle
 }
 }
 }
 

int julia(float[] z,int num){
 //runs the process num times
 //and returns the diverge count
 int count=0;
 //define z1 as z
 float[] z1 = z;
 //iterate num times
 while (count <= num){
 //check for divergence
 if (magnitude(z1) > 2.0){
 //return the step it diverged on
 return count;
 }
 //iterate z
 z1=cAdd(cMult(z1,z1),c);
 count+=1;
 }
 //if z hasn't diverged by the end
 return num;
}


float[] cAdd(float[] a,float[] b){
 float[] output = {a[0]+b[0],a[1]+b[1]};
 return output;
}

float[] cMult(float[] u,float[] v){
 //Returns the product of two complex numbers
 float[] output = {u[0]*v[0]-u[1]*v[1],u[1]*v[0]+u[0]*v[1]};
 return output;
}
 

float magnitude(float[] z){
 float output = z[0]*z[0] + z[1]*z[1];
 if (output == 0){
 return 0;
 } else {
 return sqrt(output);
 }
}