julia_set, an Octave code which computes and plots a Julia set, the set of points in the complex plane that remain bounded under a mapping of the form f(z) = z^2+c.
We consider points (X,Y) in a rectangular domain R = [XL,XR]x[YB,YT]. Here XL=-1.5, XR=+1.5, YB=-1.5, YT=+1.5.
For every (X,Y) in R, let Z be the complex number X+Yi, and let C be some complex constant. Here, C=-0.8+0.156i.
For each Z, consider the sequence of points:
Z(0) = Z,
Z(k+1) = Z(k)^2 + C
The Julia set is the set of points Z in R with the property that the sequence of points Z(k) remain within R.
To compute a picture of the Julia set, we choose a discrete array of WxH points in R. We carry out up to 200 steps of the iteration for each point Z. If 1000 < |Z| at any time, we assume Z is not in the Julia set.
The computer code and data files described and made available on this web page are distributed under the MIT license
julia_set is available in a C version and a MATLAB version and an Octave version.
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