Do they still make screensavers that collect these kinds of things these days? When I was a kid, I used to love just staring blankly at computer screensavers.
That is some hubris for Paul to claim to have “created” this fractal in December 2020. Yes he coded up and rendered some nice images from this particular function. But this class of rational maps in complex dynamics has been studied by actual mathematicians for decades and there are many extremely similar visualizations. It’s a nice little exercise but there’s very minimal real original contribution that deserves attribution here.
You could render this in Fractint in DOS just by plugging that function in, I explored many similar cubic fractals with Fractint back in the mid-90s. And would have earlier if my parents could have afforded a 386 before then. It was released in 1988.
Fractal Domains
Exploring fractals with your Macintosh
Triple Dragon
September 3, 2006
Click image to see full size
Julia set using square orbit trap. The formula used was
f(z) = z^3/(z^3 + 1) + c, c = 0.18 + 0.68 i
Downloads and extras
“Triple Dragon” Parameter File
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.
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.
Like that complete FRAUD, Leonardo da Vinci, who simply repainted a depiction of 12 apostles seated on one side of a dinner table, with their leader Jesus at the center.
He didn't even create the pigments - those were formed by natural Earth geology!
They weren’t “my” cubic fractals in the mid-90s any more than Paul “created” a fractal out of z^3/(z^3+1) + c in 2020. Pretty pictures on his blog are fine, giving it a name and attributing himself as its “creator” when this was well-explored decades earlier with better renderings is the hubris.
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.
Always love to see new stuff on Paul Bourke's web site!
Probably the first non AI-generated graphic I've seen in a year! :)
>AI
Assorted Imaginaries?
Do they still make screensavers that collect these kinds of things these days? When I was a kid, I used to love just staring blankly at computer screensavers.
ElectricSheep (https://electricsheep.org/) is still around. Based on fractal flames (https://en.wikipedia.org/wiki/Fractal_flame). Freaks out corporate firewalls though, because it looks a lot like a file sharing network.
thanks!
Fun fact, the frontier LLMs can (mostly) oneshot a realtime implementation of it (I got passable versions in both webgl and in c++ for a screensaver).
They struggle with the "evolution"/variation part, though, so you mostly get some fixed number of variants.
That is some hubris for Paul to claim to have “created” this fractal in December 2020. Yes he coded up and rendered some nice images from this particular function. But this class of rational maps in complex dynamics has been studied by actual mathematicians for decades and there are many extremely similar visualizations. It’s a nice little exercise but there’s very minimal real original contribution that deserves attribution here.
You could render this in Fractint in DOS just by plugging that function in, I explored many similar cubic fractals with Fractint back in the mid-90s. And would have earlier if my parents could have afforded a 386 before then. It was released in 1988.
He retained the original name, from 2006 ...
https://au.pinterest.com/pin/triple-dragon--1742330793037990... fractaldomains.com Triple Dragon Triple dragon fractal. Equation: f(z) = z^3/(z^3 + 1) + c, c = 0.18 + 0.68 i
https://www.fractaldomains.com/2011/08/triple-dragon/
https://web.archive.org/web/20200000000000*/https://www.frac... https://web.archive.org/web/20200209172651/http://www.fracta...
Fractal Domains Exploring fractals with your Macintosh
Triple Dragon September 3, 2006 Click image to see full size
Julia set using square orbit trap. The formula used was f(z) = z^3/(z^3 + 1) + c, c = 0.18 + 0.68 i Downloads and extras “Triple Dragon” Parameter File
Copyright © 2011 Dennis C. De Mars
triple-dragon.zip : 1058 3-Sep-2006 20:06:36 Triple Dragon DMrsFra2...
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Paul's image is a nice rendering of an attractive fractal.
I reckon Paul only claims to have created the webpage titled 'Triple Dragon Fractal'.
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/
I take it he claims to have created these particular pictures of the fractal, which is likely true. And yes, the webpage containing them as well.
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/
Like that complete FRAUD, Leonardo da Vinci, who simply repainted a depiction of 12 apostles seated on one side of a dinner table, with their leader Jesus at the center.
He didn't even create the pigments - those were formed by natural Earth geology!
[flagged]
They weren’t “my” cubic fractals in the mid-90s any more than Paul “created” a fractal out of z^3/(z^3+1) + c in 2020. Pretty pictures on his blog are fine, giving it a name and attributing himself as its “creator” when this was well-explored decades earlier with better renderings is the hubris.
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/