Coloring Methods and Formulas

Both the coloring methods and the mathematical formulas available to the fractal artist determine the way the resulting image looks.  From the standpoint of the artist,  you can't divorce one topic from the other.  This section focuses on how coloring methods....ucl files in UF....and formulas .....ufm files....work together in a practical sense.  If you are interested in the more technical aspects of coloring fractals, please visit Damien Jones' wonderful (and very understandable) pages.  The images shown in this section are available for download as a zipped set of ufr files if you would like to view them in UF.  History of formulas and coloring methods, UF

Prior to the introduction of UltraFractal, most popular fractal generating programs bundled a formula together with a coloring method.  In the early days of the DOS program Fractint, only a limited number of coloring methods such as the standard and decomposition were available.  However, mathematician artists were writing their own code which applied startlingly beautiful coloring methods to the tried and true formulas like the Mandlebrot or Julia sets.  With the release of version 19.6 of Fractint, these coloring methods could be added to formulas.  While this opened up a vast new range of possibilities, the artist was still stuck with a coloring method specific to a formula.  In parallel development, Windows programs  were beginning to separate the formula from the  coloring method so that they could be re-combined at the users behest.  But the range of available formulas was severely limited.  UltraFractal brought forth the first popular departure from Fractint and offers a broad range of formulas and coloring methods, each independent from the other.  Those who like to write formulas and coloring methods can add to the ones which come with UltraFractal and a staggering number are now  available for download by following links from Janet Preslar's UF Resource page.

Basic concepts

I think of a fractal formula as a method of plotting which generates a graphic by telling the computer, put a  blue dot (pixel) here, put another  yellow one there, etc.  The arbitrator of where the pixels go is a mathematical formula just like the ones we learned in geometry class.  The most famous formulas are the Mandelbrot and Julia sets which looks like this
 


The Mandelbrot Set

The Julia Set

But there are as many possibilities available as there are formula writers.  Here are a couple of formulas from Gedeon Peteri
 


gfpcau02

gfpstr01

As you can see, a formula radically alters the shape of the fractal.  These examples use the default coloring method "none" whose name is something of a misnomer.  It is not the absence of a coloring method, but the simplest one and the one used by Fractint, so perhaps the most familiar.  What you see is a general idea of the shape generated by the formula with the coloring method instructing UF which color to use for each pixel.  The shape can be enhanced by selecting a different coloring method as I do below.
 


Julia with cardioid coloring

gfpcau02 with cardioid coloring

When you compare the version of the formula using "none" with the version using the new coloring method notice that

A coloring method will add more interest to the basic formula but it work with what is there to begin with.  So a Julia with a lot of swirls will continue to have those swirls to color and explore.  A formula like gfpcau02 will keep that heart like outline to exploit.  I'll use these two formulas as examples throughout this section so there are not too many variations to absorb at once.   We'll also use the same 4 color blue-yellow-white-orange gradient which I use as my default.  When you are exploring UF on your own, I suggest you keep as many variables constant as you can and concentrate on what's new to you.

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Color Basics|Gradients |Black|Merge Modes|Color Sets|Masking|Coloring Methods|Links and Miscellaneous


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