How to plot this fractal I'm a graphic designer and my client has asked me to use this fractal in a design that I'm working on. As you can see, it's not a very good copy, so I'm trying to see if I can generate a high-resolution version for the project. I've found all sorts of fractal generators that work great and many of them will allow me to enter a specific equation. The trouble is that I'm a designer and not a mathematician! So the question is this: is it plausible to think that this could be reverse engineered, or is that an insane idea? If it's plausible, how would I achieve it?

EDIT:
I found the original from the book (below). The values @Carlo Beenakker posted got me very close to the right area. I was able to render and warp the output and achieve what we were looking for! It's not exact, but very close.

 
 A: If the requirements are:
(a) fractal (image is repeated at small scales); and
(b) clockwise spiral
then the following may be of use:

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.
A: 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 $z_0=0.202-0.55\,i$, $n=400$.
A: It looks like a tiling of some type of julia fractals, then post-distorted with a 'spiral' map. Hence, it seems to fall in the "flame fractal" category.
The downside is that there are a lot of parameters to play around with. Also, a reverse image search gave me nothing, so this is not a picture grabbed from the internet.
There is a huge fractal art community at DeviantArt.com - if your client really want something like this, perhaps one can ask one of the artists for a commission?
Side note: I have developed some software to make this type of fractals, so I am rather familiar with the process. Also, in all fractals I generate, I hide the underlying equations as metadata in the image file, so that I can always recreate the fractal (this can be of interest for other mathematicians out there).
