%Mandelbrot set
clf
clear
xmin = -2.1;
xmax = +0.6;
ymin = -1.1;
ymax = +1.1;
%number of points = resolution in x and y direction
nPoints = 31;
%upper limit for |z|, consider series has diverged if exceeded
zmax = 1e6;
%the 'i' index walks along the 'x' direction
for i=1:nPoints
% the 'j' index walks along the 'y' direction
for j=1:nPoints
%%%% map the index 'i' onto the interval [xmin,xmax]
%%%% i=1 must yield 'xmin'
%%%% i=nPoints must yield 'xmax'
x(i) = % add line here
%%%% map the index 'j' onto the interval [ymin,ymax]
%%%% j=1 must yield 'ymin'
%%%% j=nPoints must yield 'ymax'
y(j) = % add line here
c = complex(x(i),y(j)); % this converts (x,y) to a complex number 'c'
z = complex(0.0,0.0); % iteration starts with complex number = 0
it_max = 50; % no more than 50 iterations please
for n = 1:it_max
%%%% add the iteration formula for the Mandelbrot set
z =
if (abs(z)>zmax) % stop the iteration of z exceed limit
break;
end
end
%store the results in the matrix ZZ(nPoints,nPoints)
if (abs(z)<=zmax) ZZ(j,i)=0; % make it '0' for blue if |z| is small and series has not diverged
else ZZ(j,i)=1; % make it '1' for red if |z| is large and series has diverged
end
end
fprintf('Iteration %d\n',i);
end
imagesc(x,y,ZZ); % plot the image