4 ms·

The first Mandelbrot generator I played with took more than 3 hours on a BBC Micro to render a 160x256 image. That was 30 years ago and I still try out variatio

The first Mandelbrot generator I played with took more than 3 hours on a BBC Micro to render a 160x256 image. That was 30 years ago and I still try out variations on this from time to time (larger exponents, fractional exponents, complex exponents, animations, etc). http://alquerubim.blogspot.com.br/search/label/Fractais http://alquerubim.blogspot.com.br/search/label/Fractais

Theodores 9y ago
I was there too. Plus at the time Mandelbrot was new, as new as Deepdream images are today. So the Alto must pre-date Mandelbrot sets and therefore this demo is non-canonical, like playing Tetris on it, not possible at the time or even imagined.
- dave_sullivan 9y ago
  This reminded me of an interview w/ Carl Sagan, Stephen Hawking, and Arthur C Clarke from 1988. Clarke demos the Mandelbrot set and is clearly very excited. If only they knew... https://youtu.be/1srEEbB_vrI?t=18m31s https://youtu.be/1srEEbB_vrI?t=18m31s
  - jacquesm 9y ago
    Hawking knows.
- murbard2 9y ago
  Google image did not disappoint https://s-media-cache-ak0.pinimg.com/736x/7d/88/3f/7d883f90086c6e3cafaf2e5a90529066.jpg https://s-media-cache-ak0.pinimg.com/736x/7d/88/3f/7d883f900... https://images-cdn.9gag.com/photo/aX9BeN2_700b.jpg https://images-cdn.9gag.com/photo/aX9BeN2_700b.jpg
- grkvlt 9y ago
  The Alto was introduced in 1973, but was still available in the early 80s, so there is every possibility that someone wrote a Mandelbrot generator on it since it was discovered in 1980. However it is more likely that this happened on the Xerox Star which was around from 1981 and also after 1985 when the first popular Scientific American article about the set appeared...
keithpeter 9y ago
Yup - did that, and it was a lot faster on an Archimedes A310, I recollect minutes rather than hours and that was without the FPA unit.
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.
DanBC 9y ago
This used to be a rite of passage for programmers of the time. One example would be the advice given by Scientific American's A.K. Dedney's "Computer Diversions" Here's a 2010 reprint of a 1985 article: https://www.scientificamerican.com/article/mandelbrot-set/ https://www.scientificamerican.com/article/mandelbrot-set/ And "Fractint" (a fast viewer for many fractal types) was my introduction to open source, although they called it "stone soup". https://en.wikipedia.org/wiki/Fractint https://en.wikipedia.org/wiki/Fractint
- ghaff 9y ago
  Fractint was, if not a killer app, really popular for EGA on PCs. Compute was getting fast enough at about the same time that the computations weren't too excruciating and EGA cards were the first mainstream graphics that Mandelbrot etc. sets looked decent.
Retric 9y ago
It crazy how far computers have improved so this is the kind of thing you can do as a hobby project. https://m.youtube.com/watch?v=0jGaio87u3A https://m.youtube.com/watch?v=0jGaio87u3A
astrodust 9y ago
I remember trying to do this on a 286 and it would take the better part of a day to do an EGA quality image. A friend at the time had a 386 and it seemed blazing fast, it would take only a few hours to do a 640x480 VGA image. Now you can do this real-time on the GPU: https://www.shadertoy.com/view/4df3Rn https://www.shadertoy.com/view/4df3Rn

Theodores 9y ago

I was there too. Plus at the time Mandelbrot was new, as new as Deepdream images are today. So the Alto must pre-date Mandelbrot sets and therefore this demo is non-canonical, like playing Tetris on it, not possible at the time or even imagined.

dave_sullivan 9y ago
This reminded me of an interview w/ Carl Sagan, Stephen Hawking, and Arthur C Clarke from 1988. Clarke demos the Mandelbrot set and is clearly very excited. If only they knew... https://youtu.be/1srEEbB_vrI?t=18m31s https://youtu.be/1srEEbB_vrI?t=18m31s
- jacquesm 9y ago
  Hawking knows.
murbard2 9y ago
Google image did not disappoint https://s-media-cache-ak0.pinimg.com/736x/7d/88/3f/7d883f90086c6e3cafaf2e5a90529066.jpg https://s-media-cache-ak0.pinimg.com/736x/7d/88/3f/7d883f900... https://images-cdn.9gag.com/photo/aX9BeN2_700b.jpg https://images-cdn.9gag.com/photo/aX9BeN2_700b.jpg
grkvlt 9y ago
The Alto was introduced in 1973, but was still available in the early 80s, so there is every possibility that someone wrote a Mandelbrot generator on it since it was discovered in 1980. However it is more likely that this happened on the Xerox Star which was around from 1981 and also after 1985 when the first popular Scientific American article about the set appeared...

keithpeter 9y ago

Yup - did that, and it was a lot faster on an Archimedes A310, I recollect minutes rather than hours and that was without the FPA unit.

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.

DanBC 9y ago

This used to be a rite of passage for programmers of the time. One example would be the advice given by Scientific American's A.K. Dedney's "Computer Diversions" Here's a 2010 reprint of a 1985 article: https://www.scientificamerican.com/article/mandelbrot-set/ https://www.scientificamerican.com/article/mandelbrot-set/ And "Fractint" (a fast viewer for many fractal types) was my introduction to open source, although they called it "stone soup". https://en.wikipedia.org/wiki/Fractint https://en.wikipedia.org/wiki/Fractint

ghaff 9y ago
Fractint was, if not a killer app, really popular for EGA on PCs. Compute was getting fast enough at about the same time that the computations weren't too excruciating and EGA cards were the first mainstream graphics that Mandelbrot etc. sets looked decent.

Retric 9y ago

It crazy how far computers have improved so this is the kind of thing you can do as a hobby project. https://m.youtube.com/watch?v=0jGaio87u3A https://m.youtube.com/watch?v=0jGaio87u3A

astrodust 9y ago

I remember trying to do this on a 286 and it would take the better part of a day to do an EGA quality image. A friend at the time had a 386 and it seemed blazing fast, it would take only a few hours to do a 640x480 VGA image. Now you can do this real-time on the GPU: https://www.shadertoy.com/view/4df3Rn https://www.shadertoy.com/view/4df3Rn