Apophysis

Apophysis is a program for creating fractal flames, similar to FLAM3. It's free to download and relatively simple to use -- it's possible create interesting compositions without much knowledge of the program or the mathematical concepts behind it.

The program is based on fractals. A fractal is a geometric shape that's very complex and often appears in nature. Fractals are typically self similar, meaning (in simple terms) that they can be constructed out of infinite quantities of smaller versions of themselves. I've been looking around, and I've discovered that it has something to do with the concept that if one were to continually decrease the unit of measurement on a jagged object, the object would be infinitely large (The Coastline Paradox.) Some common examples of fractals include the Sirpinski Triangle and Koch's Snowflake. . Fractals can have fractional dimension... a concept which I'm still working to understand..but instead of being 1D or 2D or even 3D... they can have non integral dimensions, if fractal dimension is defined as the "log of the number of self similar pieces divided by the log of the magnification factor" (taken from http://math.bu.edu/DYSYS/chaos-game/node6.html#SECTION0006000000000000000)
 ... If you want to understand the math better, I'd suggest you go hunting yourself. It's difficult to teach about a topic I don't nearly grasp myself.

Apohysis crates, as I stated above, fractal flames. Fractal flames are a type of iterated function system (IFS.) An IFS is a fractal constructed by the combination of several copies of itself, the Sierpinski Triangle being an example. (Wait a second... then what makes it necessary to call an iterated function system an iterated function system and not a fractal? No clue. Fractal flames differ from normal iterated function systems, all though the information as to how they do so does not yet make sense to me, so I won't share it with you. You can look on your own. The Wikipedia page on fractal flames has fantastic information about the mathematics behind the functions used in the program.

Apohysis then, is a fractal editor.

This is the Editor box in the program. As you can see, it's based off of triangles which you can modify- position, dimensions, rotation, etc. You can add triangles and delete them, too. That in turn influences the flame. Under name, you have several options you can apply to your flame, from items like swirl and spherical to gaussian blur. I suppose that perhaps these are shapes and photoshop-esque filters you can apply to the appearance of your flame, but I haven't experimented with the program enough to know exactly what they do. You can influence the values of each of these options as well.

This is the adjustment window. In gradient, you can influence color scheme. Brightness, in the flame above, seemed to influence the brightness at the center, which in turn radiated outward. Vibrancy, on the other hand, seemed to influence the brightness of each individual pixel of the flame. Gamma seems to influence the concentration of the pixels. When brought up, the pixels spread out. When brought down, they concentrate towards a center.

The program also provides a set of mutations you can apply to the flame as you progress through its creation.

It's difficult to apply constraints to the program, or define exactly what it does. It's something you play with, and things turn out.

The program is used for making things like nebuli... or is it nebulas? I'm not sure. It's also used for artwork. ElectricSheep uses it to make screen savers

I encourage you to try it!!!

Wow, what a post! Took me a while!

Have fun!

-Yume