The source info (<A HREF="https://en.wikipedia.org/wiki/War_in_the_Age_of_Intelligent_Machines">War in the Age of Intelligent Machines</A>) identifies the fractal as a <A HREF="https://en.wikipedia.org/wiki/Julia_set">Julia set</A>, 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 <A HREF="https://pixels.com/featured/fractal-geometry-julia-set-image-lifesmith-classic-fractalsscience-photo-library.html">pixels.com</A> and could create an image such as this.

<IMG SRC="https://ilorentz.org/beenakker/MO/Julia_spiral_2.jpg"/>

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 $z_0=0.202-0.55\,i$, $n=400$.