Kickstarter

Since a number of backers have asked about the "formula" for the image, I thought I should do an update on the issue for general information of all backers.

There are two elements to the math. The algorithm, which is called the "flame fractal algorithm" and the parameters or values that are used for each individual image. The algorithm is the computer program that renders the image. It is an iterative function system or IFS for short.  There is a good description of it in wikipedia under flame fractal. It is a program that randomly samples from a space that has been influenced by various non-linear functions that are weighted relative to each other. Each pixel in the image has several counters on it, and all sorts of things are done with the pixel hits frequencies.

The individual parameters, that is, exactly which functions are used (there are about a hundred to choose from at present), and exactly how they are weighted relative to each other, are included in the header of the JPEG file. Just click on file properties. These usually run four or five pages of numbers, and they are not the program, just the values of the functions used in this particular image. The actual calculations, or iterations, are not included, since there are trillions of them in the "rendering". The poor computer runs for 24 hours or more, at 3 million calculations per second.

Sorry if this sounds complicated, it just is. That is why the images look so fantastic.

Bob Jansen