有没有更简单的方法在Matlab中构造Mandelbrot集？

Question

下面显示的代码用于绘制Mandelbrot集,我认为我的代码有点冗余来构建Matrix M.在Python中,我知道有一个干净的方法,

M = [[mandel(complex(r, i)) for r in np.arange(-2, 0.5,0.005) ] for i in np.range(-1,1,0.005)]

在Matlab中有类似的方法吗？

function M=mandelPerf()
rr=-2:0.005:0.5;
ii=-1:0.005:1;
M = zeros(length(ii), length(rr));
id1 = 1;
for i =ii
    id2 = 1;
    for r = rr
        M(id1, id2) = mandel(complex(r,i));
        id2 = id2 + 1;
    end
    id1 = id1 + 1;
end
end

function n = mandel(z)
n = 0;
c = z;
for n=0:100
    if abs(z)>2
        break
    end
    z = z^2+c;
end
end

Answer 1

你可以完全避免循环.您可以z = z.^2 + c以矢量化方式进行迭代.为了避免不必要的操作,在每次迭代时c都要跟踪哪些点已超过您的阈值,并继续仅使用其余点进行迭代(这是索引的目的,ind并ind2在下面的代码中):

rr =-2:0.005:0.5;
ii =-1:0.005:1;
max_n = 100;
threshold = 2;
c = bsxfun(@plus, rr(:).', 1i*ii(:)); %'// generate complex grid
M = max_n*ones(size(c)); %// preallocation.
ind = 1:numel(c); %// keeps track of which points need to be iterated on
z = zeros(size(c)); %// initialization
for n = 0:max_n;
    z(ind) = z(ind).^2 + c(ind);
    ind2 = abs(z(ind)) > threshold;
    M(ind(ind2)) = n; %// store result for these points...
    ind = ind(~ind2); %// ...and remove them from further consideration
end

imagesc(rr,ii,M)
axis equal