In high school, I spent some time generating fractales, mostly using Javascript and the web worker API. Some of the results are in the gallery and around the website. I based myself on a pdf by Draves and Reckase. Their technique, called fractale flame, gives beautiful fractales with very nice colors. It is based on a classical iterated function system, where the functions are allowed to be non linear. The vibrant colors are due to a simple trick. The brightness of a point is given by the log-density of amount of times it was visited instead of a linear density or none. Under are 3 different examples.
After clicking “Lancer”, waiting a moment and “Rendu”, we get the following image which is the Sierpiński triangle.
It is possible to set precise coordinates to get a more aligned image and to use gamma correction to make it look brighter. It is not possible to get all the images in the gallery using this app but one can get Barnsley’s fern and a lot of other nice images, when playing a bit.
Here are a few codes that you can input under “Charger” and see how it looks like:
- 0:0:1:1:500:500:10000:0.8:1,1;0;0:0;1:0;0.5:0;0:1;1,1;0;0:1;0:0.5;0:0;0:1;1,1;0.5;0:0.6;0.6:0;0.5:0.4;0.4:0.5;0
- 0:0:1:1:500:500:10000:0.8:1,0;0;1:0;1:0;0.5:0;0:1;1,0;0;1:1;0:0.5;0:0;0:1;1,0;0;1:0.3;0.3:0.2;0.8:0.7;0.7:0.8;0.2
- -1:-1:1:1:500:500:100000:0.7:1,1;1;0.5:-1;1:-1;0:-1;-1:0;0,1;1;0.5:-1;-1:0;-1:1;-1:0;0,1;1;0.5:1;-1:1;0:1;1:0;0,1;1;0.5:1;1:0;1:-1;1:0;0,1;0;0:-0.5;0.5:0;0:0.5;-0.5:-0.5;-0.5,1;0;0:-0.5;-0.5:0;0:0.5;0.5:0.5;-0.5,1;0;0:0.5;-0.5:0;0:-0.5;0.5:0.5;0.5,1;0;0:0.5;0.5:0;0:-0.5;-0.5:-0.5;0.5
- This one is in the gallery: 0:0.28:1:0.8425:1920:1080:100000:1:1,1;1;1:0.32;0.782:0.762;0.78:0.578;0.252:0.578;0.252,1;1;1:0.198;0.334:0.448;0.552:0.41;0.398:0.28;0.544,1;1;1:0.002;0.992:0.992;0.006:0.998;0.994:0.01;0.016,1;1;1:0.204;0.95:0.92;0.954:0.944;0.044:0.924;0.606,1;1;1:0.786;0.96:0.006;0.95:0.018;0.448:0.016;0.05
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