I have work in Beauty of Fractals, I was 18, a fresh faced Midwest geeky punker that got his mind blown by participating in a "math research program" operating out the of Boston University Graphics Lab. It seemed like nonsense, tracking computations with trigonometry functions given imaginary numbers, but the images: this was the first time many of the easily recognized fractal shapes were ever seen. Mandelbrot and DeVanney knew the imagery would be complex interesting, but did not expect the fantastic fractals we all know now. Fun times, indeed.

This is an amazing comment and I would really like to read more if you ever have time to write something up!

Your comment prompted me to do some web searching for documents from our work. Here's a YouTube video of a presentation/lecture we made at the B.U Graphics Lab then, with one of our first rendered fractal animations at the 2:30 mark. I remember working on this. We had AED graphics terminals (able to display 256 colors!) connected to an IBM 3090 mainframe. With special priority, our processes calculating a fractal would only require a few minutes per frame at 256x256 resolution.

https://www.youtube.com/watch?v=6QIhaDvTHXk

I fucked up once, trying to create a 256x256x256 fractal volume. How we were calculating them then was not optimized, and the hardware then is a fraction of the phone you own, and that hardware then was shared across the entire university... After my priority process calculating that 3D fractal volume was killed, because it ground the entire University Computing Center to a halt, the post mortem calculated how long the process would have required: 36 years. It would not be done yet if left running. Oops.

The Computational Beauty of Nature (published by MIT) belongs on anyone's list as well. It walks instructively through several different kinds of complex systems, including L systems, agents (Boids), cellular automata, fractals, chaotic attractors...

Na, the Lindenmayer book was much better. I own them all, and even assisted the authors at a conference where we invited all those fractal heros then. Benoit's book is the very best of these.

It inspired me to produce lots of AutoLisp for the algorithmic simplicity of city planning or architecture. Simple recursive rewriting systems. The problem starts when you need to detect 2d or 3d patterns, and expand them within the steps. This example showed that you only need 1d to create 3d and more. Simply expand the dimensions at the end.

Thanks! I just ordered "The Algorithmic Beauty of Plants" after reading the OP then saw your comments. Would you recommend one of these more than the others?

It's worth looking at ahem unauthorised versions before buying, just to check what they're like.

The Beauty of Fractals contains a lot of colour plates with images that were remarkable for 1986. There's plenty of math on every page. (It really crams a lot of math in).

The Science of Fractal Images is a bit longer. It has fewer colour plates. There's a bit less math (or maybe it's just spread out a bit more?) and there are some pseudo-code descriptions of algorithms.

The other two are much lighter. AK Dewdney's books were aimed at general readers of Scientific American who had access to a home computer. Computers, Pattern Chaos, and Beauty is eclectic. There's some math, and plenty of pseudocode examples.

Being honest: I don't know how well they've aged. Other people might have better descriptions, or alternative suggestions?

Very helpful, thank you!