Paul Bourke

paulbourke.net · Personal blog · on HN since 2011

Paul Bourke's personal site collects pages on fractals, attractors, PostScript, planetarium dome projection, geometry, and graphics.

What HN saysCommenters describe it as one of the best information sources of the 90s web and praise its content despite a dated look.
79HN people shared it
49linked it in comments
32stories submitted
1.2Kstory points
4 months agolast shared
2011people per year2026

Most-shared posts

  1. 1
    P a u l B o u r k e – Personal Pages
    5 people · 3 points · first shared 2016 · discussion on HN
  2. 2
    Fractals
    5 people · first shared 2022
  3. 3
  4. 4
    PostScript Tutorial (1998)
    3 people · 3 points · first shared 2021 · discussion on HN
  5. 5
    Hershey Vector Font (1997)
    3 people · 2 points · first shared 2011 · discussion on HN
  6. 6
    Domes, Planetariums, Fisheye, Spherical Mirror
    3 people · 2 points · first shared 2013 · 1 comments on HN
  7. 7
    Puzzles
    3 people · 1 points · first shared 2013 · discussion on HN
  8. 8
    Tilingplane
    3 people · first shared 2023
  9. 9
    Polygonise
    3 people · first shared 2014
  10. 10
    Lsys
    3 people · first shared 2021
  11. 11
    Symmetry in Chaos
    2 people · 10 points · first shared 2023 · discussion on HN
  12. 12
    Creating AIFF Audio Formatted Files
    2 people · 4 points · first shared 2016 · discussion on HN
  13. 13
    Random space filling tiling of the plane
    2 people · 1 points · first shared 2013 · discussion on HN
  14. 14
    Obj
    2 people · first shared 2019
  15. 15
    Quatjulia
    2 people · first shared 2018

What HN people wrote when they linked it

pixelpoet · 2022-06-29
+1, learnt soooo much from it. I have this mentally categorised next to Paul Bourke's website, which was one of the best sources of information in 90s internet: http://paulbourke.net/
yoklov · 2016-03-26
And this happens regularly! I know of experts in programming languages[0], compression[1], graphics[2, 3], and computational geometry[3] who all have sites that both have excellent content, and look fairly awful. [0]: http://piumarta.com/index.html [1]: http://cbloom.com/ [2]: http://iquilezles.org/ (okay, this one doesn't look that bad in retrospect) [3]: http://paulbourke.net/
smackeyacky · 2022-12-02
It's going to be tough to find something, since most Postscript is generated (badly) rather than hand written. I had a nice hand-written logo we used to use to check if our printer queues were working back in the 1990s but I have lost it now. The following link looks OK to my eyes though: http://paulbourke.net/dataformats/postscript/
trebeljahr · 2022-10-09
I have no idea honestly... One pointer that might be worth exploring, which is not quite L-Systems but might be related is Fractal Compression. I've read that there are algorithms to compress images into a "closest" IFS – iterated function system. https://en.wikipedia.org/wiki/Fractal_compression Maybe one could come up with a way of going from an image via fractal compression to an IFS which could then be used as the basis for an L-system? Most of the L-Systems that are on this site are from Paul Bourke – http://paulbourke.net/fractals/lsys/ Which is a really awesome resource!
abdullahkhalids · 2022-08-30
A few years ago, I was working for a startup in Pakistan which was making small (5-10 person) portable planetariums. The idea was to make astronomy education accessible to people from every socio-economic background. Paul's work on this [1] was amazingly helpful to get our projection done well, and put on successful shows. Also, shout out to the European Space Agency for releasing high quality Planetarium documentaries under the CC license [2]. [1] http://paulbourke.net/dome/ [2] https://www.eso.org/public/videos/archive/category/fulldome/?&sort…
rikroots · 2022-08-07
I'm going to suggest Paul Bourke's "Fractals, Chaos, Self-Similarity" website, because I often go there to get inspiration and code snippets - http://www.paulbourke.net/fractals/ Somebody else has already mentioned the excellent @beesandbombs on Twitter. I sometimes spend too much time trying to work out how Dave achieves a particular effect - https://twitter.com/beesandbombs If you're going to be drawing into the browser using the canvas element, I suggest you check out the Slaylines canvas comparison test page. There's a link to the GitHub repo which includes links to all the canvas libraries demoed there. Try out several libraries, settle for the ones which fit easiest into your preferred working style - https://benchmarks.slaylines.io/
sizediterable · 2021-12-27
I remember there being a section demonstrating this in the manual for my TI-83 calculator [0] It prompted me to learn a bit more about IFS and discover one of my favorite fractals ever. The word "chaos" where each stroke is made up of the word "chaos" [1]. I spent a bunch of time coding up the fractals on that site [2] on my calculator [0] http://manualsdump.com/en/manuals/texas_instruments-ti-83/132084/573 [1] http://paulbourke.net/fractals/ifs/chaos_1.gif [2] http://paulbourke.net/fractals/ifs/
sn41 · 2021-01-02
Related: Postscript is a great stackbased language to learn to program in. A good initial exercise is to write a factorial function: https://www-cdf.fnal.gov/offline/PostScript/BLUEBOOK.PDF http://paulbourke.net/dataformats/postscript/
amitp · 2020-12-08
Yes, old school web! A few of the others I like: https://faculty.evansville.edu/ck6/tcenters/ ; http://paulbourke.net/ ; https://pomax.github.io/bezierinfo/ ; https://www.fieggen.com/shoelace/ ; https://www.wood-database.com/ ; http://www.oftenpaper.net/sierpinski.htm ; https://www.animatedknots.com/ . There are lots more out there but social media favors new content rather than timeless content. I want to see more pages like that so, following “Be the change that you wish to see in the world”, I am writing informational pages.
doomlaser · 2020-11-20
My favorite recent font discovery is Simplex Roman. Designed in 1967 for early CRT vector displays by Dr. A. V. Hershey (for the US Naval Weapons Laboratory!), and released into the public domain. Incredibly pleasant looking even today: http://paulbourke.net/dataformats/hershey/ OpenType conversions: https://github.com/scruss/AVHershey-OTF/tree/master/otf Reminds me of vector arcade games like Asteroids and Tempest... By the way, another cool public domain font is the one used on all US interstates — 1948! https://en.wikipedia.org/wiki/Highway_Gothic
triggercut · 2013-10-02
I would recommend you look at the work of Professor Paul Bourke at the University of Western Australia in Perth. He creates some amazing immersive environments. http://paulbourke.net/dome/ http://paulbourke.net/exhibition/domeinstall/
jashkenas · 2012-08-14
Very neat. Attractors + <canvas> are a lot of fun... My favorite is the Peter de Jong attractor, described here: http://paulbourke.net/fractals/peterdejong/ Here's a <canvas> version. Click and drag and release to re-seed the starting coordinates: http://jashkenas.s3.amazonaws.com/misc/deJong/deJong.html Here's the annotated source code: http://jashkenas.s3.amazonaws.com/misc/deJong/docs/deJong.html Edit: I've added a permalink button, so that you can link directly to interesting coordinates that you discover: http://jashkenas.s3.amazonaws.com/misc/deJong/deJong.html#599,182
magicalhippo · 2026-04-26
Didn't have much time to comment earlier, so an addendum. The intro gene was the first time I had seen real-time metaballs. The implementation, and AFAIK all real-time metaballs in the demo scene at the time, relied on the Marching Cubes[1] algorithm, detailed by Paul Bourke here[2]. At the time the algorithm was patented, though up here in the Scandinavia that was not something that would hold back some teens. You can see the characteristic artifacts of the Marching Cubes algorithm in most demos. In general metaballs is just one example of using isosurfaces for rendering[3]. Other typical applications is in visualizing partial differential equations, for example computational fluid dynamics. Often it's easier to formulate equations which govern the volume rather than the surface, and you use an isosurface technique to extract the surface you're after. A point echo of Fudge told me was that a metaball doesn't have to have a strictly positive influence, you could have one which has a negative influence. I think this is what's going on with the red metaball scene in the gene intro. Nice video, was fun to learn the origins of one of my beloved demo effects. [1]: https://en.wikipedia.org/wiki/Marching_cubes [2]: https://paulbourke.net/geometry/polygonise/ [3]: https://en.wikipedia.org/wiki/Isosurface
Ethan_Barry · 2024-06-11
You got it! By approximate category and in no particular order: ## MISCELLANEOUS - [Low Tech Magazine](https://solar.lowtechmagazine.com), a solar-powered website showcasing the amazing low-tech things you can do with a little ingenuity, - [Stephen Wolfram's Blog](https://writings.stephenwolfram.com) on math, compsci, and everything else, - [Cool Macrophotography](https://www.barrywebbimages.co.uk/Images/Macro/Slime-Moulds-Myxomycete… for amazing pictures of tiny things (WARNING: Time Sink!), ## COMPUTER SCIENCE - [While-True-Do](https://blog.while-true-do.io) has lots of stuff on Linux administration and self-hosting, - [Backend Banter](https://www.backendbanter.fm) for a great podcast on backend development, - [Two Wrongs](https://two-wrongs.com) for statistics and functional programming, - [Math ∩ Programming](https://www.jeremykun.com/) where math and programming intersect! Written by a Googler... - [Paul Bourke's site](https://paulbourke.net/) where you can get happily lost exploring old pages on every topic CS touches, - [Jason Punyon's blog](https://jasonpunyon.com) for some fun algorithms and things, - [Yossi Kreinin's blog](https://yosefk.com/blog) for C, Python, and plenty of non-technical topics, - [Adrian Sampson's academic blog](https://www.cs.cornell.edu/~asampson/blog) for an academic's perspective, - [Cool polyhedra viewer project](https://georgehart.com/virtual-polyhedra/vp.html) if you like geometry, - [Another academic blog on…
corysama · 2018-09-02
I was very fortunate. This is the machine on which I originally learned OpenGL. It was an undergrad lab job where I was paid $5/hour to eventually write http://paulbourke.net/geometry/polygonise/marchingsource.cpp But, in order to do that I had to learn how to 3D at all. The most fun I had with the machine was playing GlQuake 1 at 1280x1024 on a T1 line and bragging about it on the chat where everyone thought I was lying. Of course, a year later the 3DFX Voodoo 1 would come out and deliver approximately 1/4 the fill rate for 1/1000 the price. Besides that, it was a fine machine. Lots of cores that I didn’t know how to utilize. Occasional bugs in the OpenGL implementation that might have been me accidentally triggering edge cases. Command line compiles, gdb, lots of core dumps. SGI really lost it’s way after this. Years later they would be showing at SIGGRAPH with multi-wall-sized displays, but without the programmable shading that would be all the rage not just right then, but for the next two decades... They went so far as to publish papers showing that with hundreds of passes and temporary buffers using fixed-function shading, you could eventually get mostly the same results as the new-fangled programmable BS... The brilliant engineers of SGI soon moved on to become founding members of Nvidia, ATI, Imagination and other graphics tech companies.
mlyle · 2026-07-10
Nor does he say he was the first to create them. The bro has posted hundreds or more pictures functions, many of which are well known... But well-colored and cropped into interesting locales, and described well. Including a good article that he wrote in a 1990 magazine. https://paulbourke.net/fractals/
Sharlin · 2026-07-10
I can't even fathom how you'd end up with such crazily uncharitable interpretation to think that "Created by Paul Bourke" refers to the fractal itself, rather than those specific images of the fractal. Each and every of the fractal pages here has a similar attribution: https://paulbourke.net/fractals/
close04 · 2026-07-10
The pages [1] have a mix of "Images/Graphics by", "Compiled/Written/Created/Contributed By", and "(Fractal) Attributed to" going back to 1990. So I think that attribution refers to the content and not just the page itself. [1] https://paulbourke.net/fractals/
irq-1 · 2025-03-03
Isn't there a common convention with vertex colors, where the color is just listed after the vertex? (/a quick query) https://paulbourke.net/dataformats/obj/colour.html
a_e_k · 2024-10-08
Historically, Pixar's RenderMan defaulted to a 2x2 Gaussian filter [1], and from what I can see, that hasn't changed [2]. Essentially it uses a truncated isotropic (non-separable) Gaussian defined by exp(-2.0 * (x*x + y*y)) with a 2x2 pixel support [3], which is slightly soft and completely avoids ringing. Gaussian also plays very nicely with filtered importance sampling [4] since it has no negative lobes. (Though I remember a number of studios using RenderMan preferring filters with a bit of sharpening.) [1] https://paulbourke.net/dataformats/rib/RISpec3_2.pdf#page=40 [2] https://rmanwiki-26.pixar.com/space/REN26/19661819/Filtering [3] https://paulbourke.net/dataformats/rib/RISpec3_2.pdf#page=207 [4] https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi…
steve1977 · 2024-07-17
Well there are formats like AIFF and WAVE, see here: https://paulbourke.net/dataformats/audio/ These are more or less direct descendants of IFF so to speak (WAVE being based on RIFF, which is essentially little-endian IFF), the page also mentions as much: "Audio IFF conforms to the "EA IFF 85" Standard for Interchange Format Files developed by Electronic Arts."
Conscat · 2024-05-10
Readers might also be interested in the "spiral honeycomb mosaic" which I found from this article linked somewhere on Stack Overflow years ago. https://paulbourke.net/geometry/tilingplane/
vitiral · 2024-01-03
I found this reference for Hershey Vector font https://paulbourke.net/dataformats/hershey/ It seems to describe a "pen" which draws the character. It is indeed pretty cool!
poetaster · 2023-11-19
I think that it's actually P. Bourke's Tree : http://www.paulbourke.net/fractals/lsys/
stcg · 2023-10-20
There is a note on another page about it: https://www.redblobgames.com/grids/parts/#more > Spiral Honeycomb Mosaic [0] (search the page for "Spiral Honeycomb Mosaic") is an interesting way to assign numbers to hexagons in a hexagonal grid. It results in bizarre properties. [0] http://paulbourke.net/geometry/tilingplane/
virtualritz · 2023-10-20
This is critically missing spiral hex coordinates which require only a single coordinate, not two. I think the original idea is from Paul Bourke. He calls it a Spiral Honeycomb Mosaic (SHM). See his "Tiling on The Plane" page [1]. Scroll down to the section titled "Hexagonal Lattice" (contains links to source code with coordinate conversions). Here is a Rust implementation of a different variant of the same idea [2]. [1] http://paulbourke.net/geometry/tilingplane/ [2] https://crates.io/crates/hex-spiral
akkartik · 2022-07-24
Is there a list of awesome fractals to zoom into with Xaos somewhere? edit: Wait a minute, it's right on the same site! http://www.paulbourke.net/fractals
iliketrains · 2021-11-11
I find TGA very useful when in need of image output and without easy access to a proper image lib. TGAs are trivial to output just by writing RGB values to a file with a simple header, no encoder needed. I am so glad that many image viewers/editors still load TGA, my computer has gigabytes of them! Spec here: http://www.paulbourke.net/dataformats/tga/
ReleaseCandidat · 2021-11-10
SGIs RGB files are missing. http://paulbourke.net/dataformats/sgirgb/sgiversion.html Had been heavily used on SGIs as their 'native' image file format.

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