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.
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.
The pages [1] have a mix of "Images/Graphics by", "Written By", "Created By", and "Attributed to" going back to the early '90s. So I think that refers to more than just the page itself.
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
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!
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.
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[ 5.4 ms ] story [ 44.0 ms ] threadAssorted Imaginaries?
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.
https://paulbourke.net/fractals/
[1] https://paulbourke.net/fractals/
https://paulbourke.net/fractals/
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.
He didn't even create the pigments - those were formed by natural Earth geology!
They struggle with the "evolution"/variation part, though, so you mostly get some fixed number of variants.