10 ms·

One-Hour Mandelbrot: Creating a Fractal on the Vintage Xerox Alto

112 points by darwhy 9y ago

1001101 9y ago
"You can also see the CPU's registers on this board." That made me LOL a bit. Very interesting architecture.
- schoen 9y ago
  I've come to understand that many CPUs were not single-chip, well into the integrated circuit era. Today we might assume that a microprocessor will come in a single package, but that wasn't a reasonable assumption in other decades, where the computer designer might even be creating the CPU as well, and not have access to a semiconductor fab.
  - dbcurtis 9y ago
    Are you trying to make me feel old, simply because I once had the 74Fxxx TTL catalog nearly memorized? Or that I can do an instruction decoder and conflict interlock unit in 100K ECL? Now get off my lawn or I shall be forced to shake my cane at you quite vigorously. Honestly, those were fun, fun days.
  - kens 9y ago
    It's surprising to me how in the 1970s, if someone needed a processor for something (even a video game or CNC controller), it was normal for them to invent a new instruction set and put together a processor from TTL chips. The barrier to entry was very low.
    - cr0sh 9y ago
      > The barrier to entry was very low. If you had the money. Those chips weren't cheap back then (even the 74xx branch), and you still needed quite a few to do anything useful when it came to building a CPU.
      - grkvlt 9y ago
        Well, there's always the 74181, a 4 bit ALU[0] as used in the Alto[1] among others like the NOVA and VAX 11/780. 0. https://mil.ufl.edu/4712/docs/74LS181.pdf https://mil.ufl.edu/4712/docs/74LS181.pdf 1. https://en.wikipedia.org/wiki/74181#Computers https://en.wikipedia.org/wiki/74181#Computers
    - edmccard 9y ago
      >...put together a processor from TTL chips. The barrier to entry was very low. It was mostly because of the clock speeds, wasn't it? I seem to remember once hearing that below 20 Mhz you could play "TTL Lego" but above that you ran into problems with things like propagation delay.
      - schoen 9y ago
        The stated propagation delay for TTL chips was usually about 10 or 20 nanoseconds (sometimes larger for more complex logical operations, and frequently smaller in subsequent logic generations, like 5 nanoseconds or so). I just checked this in a late 1970s databook. So, 20 MHz seems pretty credible for a region where you would see problems due to propagation delay—maybe even somewhere below that with the original 7400 series. That's also a reason that I hadn't thought about so much why putting the whole CPU on a single die would look more and more practical over time: propagation delay in wires!
forinti 9y ago
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...
pjmlp 9y ago
Nice, just a bit disappointed it was in BCPL and not Mesa.
- kens 9y ago
  I'm working on getting Mesa and Smalltalk running on the Alto, so stay tuned... But BCPL is actually an interesting language. I knew that it influenced C (as did Algol and other languages), but until using BCPL I didn't realize how much of C was really the same as BCPL.
  - pjmlp 9y ago
    Thanks for the information, curious how it will turn out to be.
  - jacquesm 9y ago
    BCPL is almost a predecessor to C. The 8 bit micro that I used had a BCPL compiler for it. http://www.computinghistory.org.uk/userdata/images/large/PRODPIC-9770.jpg http://www.computinghistory.org.uk/userdata/images/large/PRO... That was a nice stepping stone to C on the Atari ST.
    - eschaton 9y ago
      It wasn't "almost" a predecessor to C, it was a direct predecessor.
      - pjmlp 9y ago
        There was B in between, which was Ken's attempt to a BCPL compiler, even the language's manuals look quite similar.
sp332 9y ago
And now my crummy laptop can render a smooth-shaded version full-screen at 12 FPS. https://www.shadertoy.com/view/lsX3W4 https://www.shadertoy.com/view/lsX3W4
- Asooka 9y ago
  And it does that with a brute-force algorithm. Try xaos, it can render much faster using ONLY THE CPU
TekMol 9y ago
On a modern computer, a Javascript program can generate the Mandelbrot set in a fraction of a second, while the Alto took an hour. Hm... a "fraction" could mean anything. If it's exactly a second, then the speedup factor would be about 3600x. The Alto was built about 40 years ago, right? That would be 30% performance improvement per year. Is that about right for single cpu performance acceleration over the last 40 years?
- eru 9y ago
  30% improvement for net performance might actually be about right. Raw improvements were bigger, but software got slower.
- kalleboo 9y ago
  Well with this[0] implementation[1] my laptop can render 3840x2400 pixels at 60fps, so ignoring the larger resolution, so how about 1/60th of a second? [0] https://news.ycombinator.com/item?id=14588789 https://news.ycombinator.com/item?id=14588789 [1] Is using a GPU cheating? Are we comparing computer performance or CPU performance? The Alto didn't even have a CPU as we know it today...
  - TekMol 9y ago
    [1] Well, a GPU is somewhat geared towards this kind of workload. Both comparisons (Alto to modern CPU and Alto to modern GPU) have some meaning.
DaniFong 9y ago
For anyone on iOS, I recommend you check out the app Frax. Created in part by the Legendary Kai Krause! http://fract.al/ http://fract.al/ Realtime, 60 fps, incredibly beautiful fractals on iPhone and iPad. (am not affiliated with them, just a fan)
- jw1224 9y ago
  Frax is a masterpiece. It's one of those extremely rare apps that manages to effortlessly combine extreme technical competency with a creative, intuitive and inspiring user experience. I just got a new 12.9" iPad Pro this weekend, and Frax absolutely pushes the boundaries in terms of what the iPad can do. Just the maths involved to render the light, colour, texture and movement - in real-time, at 2732x2048 resolution - blows me away. ------ EDIT: I just made this[1], and a video exploration of the fractal too[2]. [1] http://i.imgur.com/s7sNYJ0.jpg http://i.imgur.com/s7sNYJ0.jpg [2] https://youtu.be/35f6YbV39e8 https://youtu.be/35f6YbV39e8
- sp332 9y ago
  If you're not feeling so artistically inclined - or maybe just burned out on the Mandelbrot set - you can get a "flame" fractal image or video every month from a guy I know who does them professionally. https://www.patreon.com/QuinnPalmer https://www.patreon.com/QuinnPalmer
  - sp332 9y ago
    Super late edit - it's several wallpapers per month and one video. Also you can get physical objects with the designs on them through his kinda-defunct old site http://fractal.world/ http://fractal.world/
krylon 9y ago
I still remember the day I read the article on the Mandelbrot set and went, "Whoa, I understand the math!" I went on to write my first Mandelbrot renderer in Python. I was delighted, in a way, that it worked, but badly disappointed at the performance. I rewrote the thing in C, and then rewrote it again to make use of multiple CPU cores. I am certain there are Mandelbrot renderers out there that put mine to shame. But still, it was fun, and I got some pretty desktop wallpapers out of it. And I learned a thing or two along the way. Also, I rewrote it again using PVM (Parallel Virtual Machine) to spread the work out across several computers. So I actually learned two or three things along the way. ;-) In a previous job, I had a supervisor who learned programming in the mid-80s who told me about rendering the Mandelbrot set, then using bit-twiddling on the VGA memory to change the color palette on the display. I was not sure if I should be envious to have missed those times or happy.
- dekhn 9y ago
  yeah, once z = z2 + c was explained, most of Mandelbrot was easy for me too. I tried it in BASIC on an Apple IIe. it was the first time I was confronted with the question of whether it was safe to run the computer over night, or if it would overheat. The next morning, the computer was fine, but it still hadn't reached an interesting part of the set. So once I got a PC I ended up using Fractint. In those days, Intels had slow floating point, so they ported the algorithm to use integer. That was much more effective than jjust speeding up the machine clock (my first learning about performance). Palette cycling was "cool" but by the time I got to college, while I thought I'd spend all my time generating fractals, I found the real world more interesting...
pasbesoin 9y ago
Reminds me of writing programs to map the Mandelbrot and Julia sets onto the display of my Kaypro 2X. Didn't even have real bitmapped graphics -- just a way of packing... I think it was 4-pixel squares, into a character representation and then writing that. Similar to packing up bits to characters shot to some sort of dot matrix printer attached to VAX, to print out such images, a couple of years earlier. At least that generated the images more quickly. The Kaypro 2X was long in the tooth, by that point. I wonder whether it will still fire up?
- cr0sh 9y ago
  There's a "mode" if you will, on CGA cards, that involves something similar - best explained here: http://8088mph.blogspot.com/2015/04/cga-in-1024-colors-new-mode-illustrated.html http://8088mph.blogspot.com/2015/04/cga-in-1024-colors-new-m... If this hasn't already been featured on HN, I'd be surprised...
karmakaze 9y ago
With the limited computing power, they should have at least used the bilateral symmetry to halve the time.
DaniFong 9y ago
An amazing demonstration of the math behind some fractals, which runs on web gl, is Steven Witten's "How to Fold a Julia Fractal" https://acko.net/blog/how-to-fold-a-julia-fractal/ https://acko.net/blog/how-to-fold-a-julia-fractal/ Highly recommended
- sdwisely 9y ago
  I recommend these too: Coding Challenge #21: Mandelbrot Set with p5.js - https://www.youtube.com/watch?v=6z7GQewK-Ks https://www.youtube.com/watch?v=6z7GQewK-Ks VEX IN HOUDINI: MANDELBROT AND MANDELBULB - https://www.sidefx.com/tutorials/vex-in-houdini-mandelbrot-and-mandelbulb/ https://www.sidefx.com/tutorials/vex-in-houdini-mandelbrot-a... The second link is Houdini specific but you should be able to follow along with the free version on win/linux/osx.
rbanffy 9y ago
It wasn't much faster on the Apple II... Even though its BASIC interpreter used a 40-bit float, that I was downsampling the resolution to get 64-ish dithered colors, and that it was compiled down to mostly ROM calls, it took a very long time to render regions, in special those closer to the set itself. Ok. As clock-efficient as the 6502 was, it still ran at 1 MHz.
_Codemonkeyism 9y ago
I remember writing Mandelbrot on C64 and Amigas. Depending on depth you could wait some time. So it often was overnight, with a pleasunt suprise the next morning (or some ugly looking picture)
andybest 9y ago
I wonder if a more efficient microcode could be written for the Alto to optimise just for rendering Mandelbrot sets
- kens 9y ago
  The Alto has up to 3K RAM to hold custom microcode, and some programs used their own microcode for performance. So, yes it would be quite possible to speed up the Mandelbrot set with microcode. But writing Alto microcode is very difficult, so I'm not planning to do that...

112 points by darwhy 9y ago

1001101 9y ago

"You can also see the CPU's registers on this board." That made me LOL a bit. Very interesting architecture.

schoen 9y ago
I've come to understand that many CPUs were not single-chip, well into the integrated circuit era. Today we might assume that a microprocessor will come in a single package, but that wasn't a reasonable assumption in other decades, where the computer designer might even be creating the CPU as well, and not have access to a semiconductor fab.
- dbcurtis 9y ago
  Are you trying to make me feel old, simply because I once had the 74Fxxx TTL catalog nearly memorized? Or that I can do an instruction decoder and conflict interlock unit in 100K ECL? Now get off my lawn or I shall be forced to shake my cane at you quite vigorously. Honestly, those were fun, fun days.
- kens 9y ago
  It's surprising to me how in the 1970s, if someone needed a processor for something (even a video game or CNC controller), it was normal for them to invent a new instruction set and put together a processor from TTL chips. The barrier to entry was very low.
  - cr0sh 9y ago
    > The barrier to entry was very low. If you had the money. Those chips weren't cheap back then (even the 74xx branch), and you still needed quite a few to do anything useful when it came to building a CPU.
    - grkvlt 9y ago
      Well, there's always the 74181, a 4 bit ALU[0] as used in the Alto[1] among others like the NOVA and VAX 11/780. 0. https://mil.ufl.edu/4712/docs/74LS181.pdf https://mil.ufl.edu/4712/docs/74LS181.pdf 1. https://en.wikipedia.org/wiki/74181#Computers https://en.wikipedia.org/wiki/74181#Computers
  - edmccard 9y ago
    >...put together a processor from TTL chips. The barrier to entry was very low. It was mostly because of the clock speeds, wasn't it? I seem to remember once hearing that below 20 Mhz you could play "TTL Lego" but above that you ran into problems with things like propagation delay.
    - schoen 9y ago
      The stated propagation delay for TTL chips was usually about 10 or 20 nanoseconds (sometimes larger for more complex logical operations, and frequently smaller in subsequent logic generations, like 5 nanoseconds or so). I just checked this in a late 1970s databook. So, 20 MHz seems pretty credible for a region where you would see problems due to propagation delay—maybe even somewhere below that with the original 7400 series. That's also a reason that I hadn't thought about so much why putting the whole CPU on a single die would look more and more practical over time: propagation delay in wires!

forinti 9y ago

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...

pjmlp 9y ago

Nice, just a bit disappointed it was in BCPL and not Mesa.

kens 9y ago
I'm working on getting Mesa and Smalltalk running on the Alto, so stay tuned... But BCPL is actually an interesting language. I knew that it influenced C (as did Algol and other languages), but until using BCPL I didn't realize how much of C was really the same as BCPL.
- pjmlp 9y ago
  Thanks for the information, curious how it will turn out to be.
- jacquesm 9y ago
  BCPL is almost a predecessor to C. The 8 bit micro that I used had a BCPL compiler for it. http://www.computinghistory.org.uk/userdata/images/large/PRODPIC-9770.jpg http://www.computinghistory.org.uk/userdata/images/large/PRO... That was a nice stepping stone to C on the Atari ST.
  - eschaton 9y ago
    It wasn't "almost" a predecessor to C, it was a direct predecessor.
    - pjmlp 9y ago
      There was B in between, which was Ken's attempt to a BCPL compiler, even the language's manuals look quite similar.

sp332 9y ago

And now my crummy laptop can render a smooth-shaded version full-screen at 12 FPS. https://www.shadertoy.com/view/lsX3W4 https://www.shadertoy.com/view/lsX3W4

Asooka 9y ago
And it does that with a brute-force algorithm. Try xaos, it can render much faster using ONLY THE CPU

TekMol 9y ago

On a modern computer, a Javascript program can generate the Mandelbrot set in a fraction of a second, while the Alto took an hour. Hm... a "fraction" could mean anything. If it's exactly a second, then the speedup factor would be about 3600x. The Alto was built about 40 years ago, right? That would be 30% performance improvement per year. Is that about right for single cpu performance acceleration over the last 40 years?

eru 9y ago
30% improvement for net performance might actually be about right. Raw improvements were bigger, but software got slower.
kalleboo 9y ago
Well with this[0] implementation[1] my laptop can render 3840x2400 pixels at 60fps, so ignoring the larger resolution, so how about 1/60th of a second? [0] https://news.ycombinator.com/item?id=14588789 https://news.ycombinator.com/item?id=14588789 [1] Is using a GPU cheating? Are we comparing computer performance or CPU performance? The Alto didn't even have a CPU as we know it today...
- TekMol 9y ago
  [1] Well, a GPU is somewhat geared towards this kind of workload. Both comparisons (Alto to modern CPU and Alto to modern GPU) have some meaning.

DaniFong 9y ago

For anyone on iOS, I recommend you check out the app Frax. Created in part by the Legendary Kai Krause! http://fract.al/ http://fract.al/ Realtime, 60 fps, incredibly beautiful fractals on iPhone and iPad. (am not affiliated with them, just a fan)

jw1224 9y ago
Frax is a masterpiece. It's one of those extremely rare apps that manages to effortlessly combine extreme technical competency with a creative, intuitive and inspiring user experience. I just got a new 12.9" iPad Pro this weekend, and Frax absolutely pushes the boundaries in terms of what the iPad can do. Just the maths involved to render the light, colour, texture and movement - in real-time, at 2732x2048 resolution - blows me away. ------ EDIT: I just made this[1], and a video exploration of the fractal too[2]. [1] http://i.imgur.com/s7sNYJ0.jpg http://i.imgur.com/s7sNYJ0.jpg [2] https://youtu.be/35f6YbV39e8 https://youtu.be/35f6YbV39e8
sp332 9y ago
If you're not feeling so artistically inclined - or maybe just burned out on the Mandelbrot set - you can get a "flame" fractal image or video every month from a guy I know who does them professionally. https://www.patreon.com/QuinnPalmer https://www.patreon.com/QuinnPalmer
- sp332 9y ago
  Super late edit - it's several wallpapers per month and one video. Also you can get physical objects with the designs on them through his kinda-defunct old site http://fractal.world/ http://fractal.world/

krylon 9y ago

I still remember the day I read the article on the Mandelbrot set and went, "Whoa, I understand the math!" I went on to write my first Mandelbrot renderer in Python. I was delighted, in a way, that it worked, but badly disappointed at the performance. I rewrote the thing in C, and then rewrote it again to make use of multiple CPU cores. I am certain there are Mandelbrot renderers out there that put mine to shame. But still, it was fun, and I got some pretty desktop wallpapers out of it. And I learned a thing or two along the way. Also, I rewrote it again using PVM (Parallel Virtual Machine) to spread the work out across several computers. So I actually learned two or three things along the way. ;-) In a previous job, I had a supervisor who learned programming in the mid-80s who told me about rendering the Mandelbrot set, then using bit-twiddling on the VGA memory to change the color palette on the display. I was not sure if I should be envious to have missed those times or happy.

dekhn 9y ago
yeah, once z = z2 + c was explained, most of Mandelbrot was easy for me too. I tried it in BASIC on an Apple IIe. it was the first time I was confronted with the question of whether it was safe to run the computer over night, or if it would overheat. The next morning, the computer was fine, but it still hadn't reached an interesting part of the set. So once I got a PC I ended up using Fractint. In those days, Intels had slow floating point, so they ported the algorithm to use integer. That was much more effective than jjust speeding up the machine clock (my first learning about performance). Palette cycling was "cool" but by the time I got to college, while I thought I'd spend all my time generating fractals, I found the real world more interesting...

pasbesoin 9y ago

Reminds me of writing programs to map the Mandelbrot and Julia sets onto the display of my Kaypro 2X. Didn't even have real bitmapped graphics -- just a way of packing... I think it was 4-pixel squares, into a character representation and then writing that. Similar to packing up bits to characters shot to some sort of dot matrix printer attached to VAX, to print out such images, a couple of years earlier. At least that generated the images more quickly. The Kaypro 2X was long in the tooth, by that point. I wonder whether it will still fire up?

cr0sh 9y ago
There's a "mode" if you will, on CGA cards, that involves something similar - best explained here: http://8088mph.blogspot.com/2015/04/cga-in-1024-colors-new-mode-illustrated.html http://8088mph.blogspot.com/2015/04/cga-in-1024-colors-new-m... If this hasn't already been featured on HN, I'd be surprised...

karmakaze 9y ago

With the limited computing power, they should have at least used the bilateral symmetry to halve the time.

DaniFong 9y ago

An amazing demonstration of the math behind some fractals, which runs on web gl, is Steven Witten's "How to Fold a Julia Fractal" https://acko.net/blog/how-to-fold-a-julia-fractal/ https://acko.net/blog/how-to-fold-a-julia-fractal/ Highly recommended

sdwisely 9y ago
I recommend these too: Coding Challenge #21: Mandelbrot Set with p5.js - https://www.youtube.com/watch?v=6z7GQewK-Ks https://www.youtube.com/watch?v=6z7GQewK-Ks VEX IN HOUDINI: MANDELBROT AND MANDELBULB - https://www.sidefx.com/tutorials/vex-in-houdini-mandelbrot-and-mandelbulb/ https://www.sidefx.com/tutorials/vex-in-houdini-mandelbrot-a... The second link is Houdini specific but you should be able to follow along with the free version on win/linux/osx.

rbanffy 9y ago

It wasn't much faster on the Apple II... Even though its BASIC interpreter used a 40-bit float, that I was downsampling the resolution to get 64-ish dithered colors, and that it was compiled down to mostly ROM calls, it took a very long time to render regions, in special those closer to the set itself. Ok. As clock-efficient as the 6502 was, it still ran at 1 MHz.

_Codemonkeyism 9y ago

I remember writing Mandelbrot on C64 and Amigas. Depending on depth you could wait some time. So it often was overnight, with a pleasunt suprise the next morning (or some ugly looking picture)

andybest 9y ago

I wonder if a more efficient microcode could be written for the Alto to optimise just for rendering Mandelbrot sets

kens 9y ago
The Alto has up to 3K RAM to hold custom microcode, and some programs used their own microcode for performance. So, yes it would be quite possible to speed up the Mandelbrot set with microcode. But writing Alto microcode is very difficult, so I'm not planning to do that...