julia_set


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.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

julia_set is available in a C version and a MATLAB version and an Octave version.

Related Data and Programs:

julia_set_test

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Reference:

  1. Heinz-Otto Peitgen, Hartmut Juergens, Dietmar Saupe,
    Chaos and Fractals - New Frontiers in Science,
    Springer, 1992,
    ISBN: 0-387-20229-3,
    LC: Q172.5.C45.P45.

Source Code:


Last revised on 23 December 2022.