How to plot this fractal

The source info (War in the Age of Intelligent Machines) identifies the fractal as a Julia set, iterates of $z\mapsto z^2+z_0$. It has evidently been distorted (warped) to give it a 3D appearance. I played around with a spiral-shaped Julia set I found at pixels.com and could create an image such as this.

The Mathematica command
Manipulate[JuliaSetPlot[a- b*I,MaxIterations->n], {a,0,1},{b,0,1},{n,100,1000}] provides a way to find suitable values for $z_0=a-bi$ (and the iteration count $n$). I find a similar spiral for $z_0=0.202-0.55\,i$, $n=400$.


If the requirements are:

(a) fractal (image is repeated at small scales); and

(b) clockwise spiral

then the following may be of use:

enter image description here

This image is generated by the complex exponential function $\exp(z)+1+2.9i$. The resolution can be improved to whatever level you desire (given enough computing power).

Alternatively, if you had a high resolution image of one of the "islands" in your image, then you could make a lattice out of many copies of that, and then apply some sort of a spiral filter which I have seen in some graphics programs like GIMP and maybe Photoshop.

Tags:

Fractals

Computational Geometry

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