The Science of Fractal Images

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1. DanBCDec 2020
   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 AK Dewdney's Magic Machine which has a chapter about L Systems: https://www.amazon.com/Magic-Machine-Handbook-Computer-Sorce...

   And Computers, Pattern, Chaos, and Beauty by Clifford Pickover: https://www.amazon.com/Computers-Pattern-Beauty-Clifford-Pic...

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2. DanBCDec 2020
   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?

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3. DanBCJun 2017
   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

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4. DanBCDec 2016
   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"

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5. RBerenguelNov 2013
   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 ago, since then I've only worked with entire transcendental functions where potentials are harder to come by. A useful approach then is to use a bifurcation loci approximation result (like this thing I worked on for a while: http://www.maia.ub.es/~ruben/docs/20110531Centres.pdf The paper with the result kind of entered a limbo while I finished my PhD... and is still there (after all it is just like 8 pages long)

   PS: Why orange? Just to avoid using the "standard blue" used in most Beamer slides :D It doesn't look as offensive in a projector as in a screen, too.

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