3D Mandelbrot Point Cloud

Programming Questions

devinj898

in Programming Questions • 3 years ago

Hello,

I am attempting to create a 3D/4D mandelbrot, visualized through the point cloud method. If there is anyone on here experienced enough with the math, I would appreciate some suggestions.

Here is a link where the math is coming from: mandelbulb mathematics

Here is the code I currently have for computing the point cloud. In the draw function in the main sketch I simply have a 'displayptcloud();' inside of a push/popMatrix();

The main tab is this:

import processing.opengl.*;
import processing.dxf.*;
boolean record;
PFont font;
void setup() {
size(1200,800,OPENGL);
smooth();
hint(ENABLE_OPENGL_4X_SMOOTH);
noStroke();
}
void draw () {
background(0);
pushMatrix();
//navigation
translate(width/2,height/2); //translate centre to the middle of the screen
scale(3);//scale three times
translate(0,0,distance);
rotateX(alpha2);
rotateZ(alpha1);
translate(translate1-cx,translate2-cy,-cz*0); // translate everything to the centroid of the set
displayptcloud();
popMatrix();
}

the function fractalpt is this:

void fractalpt (float fractalx, float fractaly, float fractalz) {
point(fractalx,fractaly,fractalz);
}

The tab for the mouse (although this shouldn't be needed) is as follows:

float alpha1 = -158.23;
float alpha2 = 1.13;
float distance = -2500;
int mouse_x, mouse_y;
float translate1 = -1700;
float translate2 = 1242;
float cx,cy,cz; //centroid
boolean keyRelease = false;
boolean pause=false;
float time = 0;
void displayposition()
{
print(" alpha1 = "+alpha1);
print(" alpha2 = "+alpha2);
print(" distance = "+distance);
print(" translate1 = "+translate1);
print(" translate2 = "+translate2);
println(" ");
}
void keyReleased()
{
keyRelease = true;
}
void mousePressed ()
{
mouse_x = mouseX;
mouse_y = mouseY;
displayposition();
}
void mouseDragged()
{
if (mouseButton == LEFT)
{
alpha1 +=(mouse_x - mouseX)/100.0;
alpha2 +=(mouse_y - mouseY)/100.0;
}
if (mouseButton == RIGHT)
{
float msx = (mouse_x - mouseX);
float msy = (mouse_y - mouseY);
translate1 -=( cos(alpha1)*msx + sin(alpha1)*msy)*10;
translate2 -=( -sin(alpha1)*msx + cos(alpha1)*msy)*10;
}
if (mouseButton == CENTER)
{
distance +=(mouse_x - mouseX)/2.5+(mouse_y - mouseY)*10;
};
mouse_x=mouseX;
mouse_y=mouseY;
}

Thanks

Devin

------------------------------------------------------------------------------------------------------------------------------------------------------------------------

HERE is all of the math, which is definitely where the problem is:

int maxiterations = 2;
int complexx = 1000;
int complexy = 1000;
int complexz = 1000;
float newx,newy,newz;
float xmin = -2.5; float ymin = -2.0; float zmin = -2.0; float wh = 4;
void displayptcloud () {
float xmax = xmin + wh;
float ymax = ymin + wh;
float zmax = zmin + wh;
float dx = (xmax - xmin) / (complexx);
float dy = (ymax - ymin) / (complexy);
float dz = (zmax - zmin) / (complexz);
//newx = 0; newy = 0; newz = 0;
float z = zmin;
for(float k = 0; k < complexz; k++) {
float y = ymin;
for(float j = 0; j < complexy; j++) {
float x = ymin;
for(float i = 0; i < complexx; i++) {
float a = x;
float b = y;
float c = z;
//float k1,k2,k3,k4;
int n = 0;
while (n < maxiterations) {
float a2 = sq(a);
float a4 = (sq(a)*sq(a));
float b2 = sq(b);
float b4 = (sq(b)*sq(b));
float c2 = sq(c);
float c4 = (sq(c)*sq(c));
float k3 = a2 + c2;
float k2 = -sqrt( k3*k3*k3*k3*k3*k3*k3 );
float k1 = (a4 + b4 + c4) - (6.0*b2*c2) - (6.0*a2*b2) + (2.0*c2*a2);
float k4 = a2 - b2 + c2;
float newx = 64.0*a*b*c*(a2-c2)*k4*(a4-6.0*a2*c2+c4)*k1*k2;
float newy = -16.0*b2*k3*k4*k4 + k1*k1;
float newz = -8.0*b*k4*(a4*a4 - 28.0*a4*a2*c2 + 70.0*a4*c4 - 28.0*a2*c2*c4 + c4*c4)*k1*k2;
if ((sq(a)) + (sq(b)) + (sq(c)) > 64.0f) {
break;
}
n++;
}
//println("xvalue" + newx);
//println("xvalue" + newy);
//println("xvalue" + newz);
if (n == maxiterations) {
fractalpt(newx,newy,newz);
stroke(255,255,0);
} else {
}
x += dx;
}
y += dy;
}
z += dz;
}
}

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