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… while in the same era Peitgen and Richter were publishing books with detailed Mandelbrot sets in full-colour plates. What computers were they using?

by waqf 9y ago

HarryHirsch 9y ago
I remember their demos. Their secret sauce was in the algorithm, which somehow would spend little time on the featureless parts.
- bonzini 9y ago
  One simple way is to start with a largish square, say 8x8 pixels, and evaluate the Mandelbrot set at the corners. If you get the same color, paint the square in a single color. Otherwise split it in 4 smaller blocks, evaluating the set at a 3x3 grid (which is not really correct, the four squares don't actually have any corner in common, but it's twice as fast). Again if any small square has the same color at the corners, fill the block with one color. One improvement for accuracy is, if you find all four corners have the same color (no matter if it's an 8x8 or 4x4 block), pick another pixel and iterate that one; if the color doesn't match, skip the optimization. That is more expensive, up to 25%, but it can avoid mistakes in the chaotic areas of the set. And of course, the large cardioid in the center has an analytic expression, and you can skip pixels inside that area, or a conservative approximation of the area.
DanBC 9y ago
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 http://imgur.com/a/KSnDZ
- rbanffy 9y ago
  A cousin, the 4341, was my first mainframe. That was the first time I was exposed to the concept behind pg's "beating the averages article": at a time most of my colleagues were writing dBase or COBOL code, I interned with people using Cincom's Mantis. It was the Rails of the 3270.
gerdesj 9y ago
I worked in a books warehouse before college and two of their books had a little accident and ended up in the rejects bin along with some of my course texts. I lent the P and R books to someone and forgot who so actually bought them later on. They are amazing. I also remember how short things like Iterated Function System plotters could be - eg a few dozen lines of BASIC could get you a complicated fern piccy in a few seconds on a 80286. I suspect they had access to some decent Unix workstations with expensive displays. The quality of the plates was breathtaking - you can barely see the graduations in many of the images and they are totally smooth in most of them. I've just had a massive hit of nostalgia - thanks!
UncleSlacky 9y ago
I recall seeing full-colour real-time Mandelbrot set zooming and fractal landscape rendering on a Meiko Computing Surface (containing 32 or 64 Transputers, IIRC) at university, circa 1990. I studied Occam at the time but we weren't allowed to actually program the Transputers ourselves. https://en.wikipedia.org/wiki/Meiko_Scientific#Computing_Surface https://en.wikipedia.org/wiki/Meiko_Scientific#Computing_Sur...

… while in the same era Peitgen and Richter were publishing books with detailed Mandelbrot sets in full-colour plates. What computers were they using?

by waqf 9y ago

… while in the same era Peitgen and Richter were publishing books with detailed Mandelbrot sets in full-colour plates. What computers were they using?

HarryHirsch 9y ago

I remember their demos. Their secret sauce was in the algorithm, which somehow would spend little time on the featureless parts.

bonzini 9y ago
One simple way is to start with a largish square, say 8x8 pixels, and evaluate the Mandelbrot set at the corners. If you get the same color, paint the square in a single color. Otherwise split it in 4 smaller blocks, evaluating the set at a 3x3 grid (which is not really correct, the four squares don't actually have any corner in common, but it's twice as fast). Again if any small square has the same color at the corners, fill the block with one color. One improvement for accuracy is, if you find all four corners have the same color (no matter if it's an 8x8 or 4x4 block), pick another pixel and iterate that one; if the color doesn't match, skip the optimization. That is more expensive, up to 25%, but it can avoid mistakes in the chaotic areas of the set. And of course, the large cardioid in the center has an analytic expression, and you can skip pixels inside that area, or a conservative approximation of the area.

DanBC 9y ago

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 http://imgur.com/a/KSnDZ

rbanffy 9y ago
A cousin, the 4341, was my first mainframe. That was the first time I was exposed to the concept behind pg's "beating the averages article": at a time most of my colleagues were writing dBase or COBOL code, I interned with people using Cincom's Mantis. It was the Rails of the 3270.

gerdesj 9y ago

I worked in a books warehouse before college and two of their books had a little accident and ended up in the rejects bin along with some of my course texts. I lent the P and R books to someone and forgot who so actually bought them later on. They are amazing. I also remember how short things like Iterated Function System plotters could be - eg a few dozen lines of BASIC could get you a complicated fern piccy in a few seconds on a 80286. I suspect they had access to some decent Unix workstations with expensive displays. The quality of the plates was breathtaking - you can barely see the graduations in many of the images and they are totally smooth in most of them. I've just had a massive hit of nostalgia - thanks!

UncleSlacky 9y ago

I recall seeing full-colour real-time Mandelbrot set zooming and fractal landscape rendering on a Meiko Computing Surface (containing 32 or 64 Transputers, IIRC) at university, circa 1990. I studied Occam at the time but we weren't allowed to actually program the Transputers ourselves. https://en.wikipedia.org/wiki/Meiko_Scientific#Computing_Surface https://en.wikipedia.org/wiki/Meiko_Scientific#Computing_Sur...