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