How do I make a high quality mandelbrot set?

I've managed to create a good-quality version of the mandelbrotset. But i'd like to go deeper, this is what i have thusfar:

clc
clear
close all

detail = 3201; %level of detail you want
a = linspace(-1.6,1.6,detail); %imaginary axis
b = linspace(-2,1.2,detail); %real axis
B = zeros(detail,detail,3); %for color mapping (have plans with the 3 colors later)
% look at "the dark side of the mandelbrot on youtube
[x,y] = meshgrid(a,b); %to create the complex plane
C = y+x*i;              %creating the plane

X = C;                  %initial conditions (first iteration)
for n = 1:63                    %iterating
  X = X.^2 + C;               %calculating
  expl = find(abs(X)>2==1);   %finding exploded values
  X(expl) = 0;                %removing from iteration
  C(expl) = 0;                %removing from plane
  B(expl) = n;                %saving step value
end

B = B/max(max(max(B)));         %deviding by max value for correct color
image(B)                        %printing

but when trying:

detail = 0.0001;

I run out of memory, i want to make it higher quality, I've thought about cutting it up and rendering smaller parts, but don't know how to connect multiple images without needing a massive array/color map (B in my case).

I haven't found anyone creating higher quality fractals, how can i improve?

Best regards, Mathieu

[Sudarshan Kolar]

You are using 'detail' with linspace. linspace(-1.6,1.6,0.0001) will try to make 0.0001 elements between -1.6 and +1.6 and will create empty 'a' and 'b'. I think you should put

detail = 10000;

Also, try increasing your Java Heap Memory.

Answer 1

[abd abd1]

hi..... here is my code in MATLAB for julia set in complex domain

for ImageWidth = 1:640
for ImageHeight = 1:480
RealPart = (ImageWidth - 320) / 120;
ImaginaryPart = (ImageHeight - 240) / 120;

iteration=0;
c=complex(RealPart,ImaginaryPart);
%z=0+0i;
k=.327+.22i;
z=c;
for i = 1:90   
    z=z^1.7+k;
    if abs(z) > 2 ,break,end
    iteration=iteration+1;
    ComplexModulusImage(ImageHeight,ImageWidth)=abs(z);
end
IterationImage(ImageHeight,ImageWidth)=iteration;%the number of iteration

end

end
ComplexModulusImage=round(ComplexModulusImage);

 image(IterationImage)
 colormap(jet)

[darova]

I suggest you to preallocate matrices for better performance

W = 640;
H = 480;
ComplexModulusImage = zeros(H,W);
IterationImage = zeros(H,W);