Forum: Fractals


Subject: Where do "Bring it in" images belong?

Deagol opened this issue on Oct 03, 2004 ยท 24 posts


TheRingess posted Wed, 06 October 2004 at 1:01 PM

Attached Link: http://markch85712.home.mindspring.com/utility.html

Hmmm....just thought I'd add my 2 pennies here. First....thanks to everyone who finds BringItIn useful. As someone has pointed out, BringItIn generates a custom coloring algorithm. Long time users of UF will know what that statement means, but non-users or beginners might not. In short, any fractal can be broken down into two basic parts, the formula that is used to generate it and the method used to determine how the pixels on the screen are colored. For example, the now famous formula z = z^2 + C is an example of a fractal formula. Basically, fractals work, by assigning two numbers to every pixel on the screen, and then for each pixel on the screen use those numbers as a starting point in an iterated process. Since theoretically, the computer could do this until the sun burns out, we need to specify when to stop and move on to the next pixel. This is done in one of two ways. We specify a condition based on the values of the numbers we are calculating, if this condition is met, in general the pixel is labeled an "Outside" point. Instead, if we hit a pre-determined number of iterations, then the pixel is labeled an "Inside" pixel. The first and simplest coloring algorithm for the Mandelbrot set was to color Inside pixels black and outside pixels white. Another simple coloring method, is to color Inside pixels black and then color outside pixels based on how many iterations we needed to perform before we determined that the pixel was Outside. More complex algorithms, use the values of the numbers at each iteration and then determined the colors based on certain functions applied to those values. These in general are called Trap Coloring methods. There are numerous examples of these types as well as hybrids in the UF formula database. To make a long story short, the coloring algorithm that BringItIn generates, is a very simple Trap Coloring method, and only differs from other coloring methods in how it calculates the color of each pixel in the screen. Basically it determines the color based on a value in a table. So theoretically, the algorithm does not even need to be associated with a picture. It could use a table filled with random colors, which might produce interesting textures. In other words, a picture generated from UF with a layer that was created by BringItIn is as much a fractal as any other picture generated by UF. I look at Keith's picture, and I guess that he used a basic Julia formula. Used BringItIn and a picture of flowers and created a custom layer in UF. Perhaps he tweaked the variables for that layer until he got what he wanted and then added other layers for other effects. It looks to me like the object pictured has a fractional dimension as well as incredible self-similarity. So it looks like its a fractal. I've uploaded XD pictures that probably weren't even fractals, but I didn't know where else to put them. Off topic, if anyone has figured out some nice modifications to the basic formula generated by BringItIn and would like to share them, I'd be more than happy to incorporate them into a new version. I'm considering adding some parameters to the formula that use the iteration information to merge colors in the gradient with colors in the picture and see if interesting effects can be produced with that. I have to find the time. Take care everyone