The Science of Fractal Images
by Heinz-Otto Peitgen, Dietmar Saupe, Yuval Fisher · first published 1988
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This is one of the trio of great books that Springer Verlag produced around the same time. The other two are The Science of Fractal Images and Beauty of Fractals. https://www.springer.com/gp/book/9781461283492 https://www.springer.com/gp/book/9783540158516 Two other books that I think are good (but which are for general audiences) are…
on “The Algorithmic Beauty of Plants (1990)” ↗They reference IBM labs. The Beauty of Fractal Images talks about an IBM 4361-5 with extended precision, and an IBM 4250 printer for one of the monochrome plates near the end of the book. The Science of Fractal Images lists, as credits for the colour plates, these people and institutions: http://imgur.com/a/KSnDZ
on “One-Hour Mandelbrot: Creating a Fractal on the Vintage Xerox Alto” ↗…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.…
on “The Algorithmic Beauty of Plants (1990)” ↗Loved the discussion of distance estimator formulae. As I recall them, to derive one of the results in The Science of Fractal Images you'd need to use Koebe's 1/4th theorem applied to the potential function (or a related function which is analytic) and thus you'd solve the factor problem. It's a little hazy, since I did this 6 years…
on “The Mandelbulb” ↗Midpoint displacement is mentioned in The Science of Fractal Images (and the Beauty of Fractal Images), and also in Mandelbrot's book Fractal Geometry of Nature. From a phone, sorry about upside down: http://m.imgur.com/JGCpnIu A snippet from "Science of Fractal Images"
on “2D Terrain generation using midpoint displacement” ↗