Formulizer

An incubator and evolutionary tool for mathematically generated bitmaps. The images are produced by a single line of code, a mathematical formula that transforms the x/y coordinates and the width and height data of the image into complex forms. For a gallery of discovered images check out formulizer.tumblr.com

Usage:
Press "Randomize Formula" to generate a new formula. Since the formula is entirely random (though syntactically correct) there is a good chance that you will either not see anything or that the resulting image is rather dull. Actually probably only 1 in 50 random formulas will look somewhat interesting. See this more like gold digging where you have to wade through a lot of dirt to find that one nugget.

There are several typical patterns that will show up most of the times: a single color, simple gradients, stripes or checkerboards. The Pascal triangle does also quite often show up. Personally I'm most interested in images that show glitches or do have no obvious pattern since those are the more rare ones.

The "Complexity" slider lets you roughly control how big the formula gets, bigger formulas might result in more complex images but it also increases the chance that one little part of it messes everything else up.

Each function contains numeric values that have a big influence on the final result, sometimes a difference of 1 can alter the entire appearance. You can change those values by either changing the numbers in the highlighted numeric tickers or by changing multiple of them randomly by pressing the "Randomize Factors" button.

In general a good approach is to randomize the formula until a halfway interesting image comes up and then to fine-tune it by randomizing or hand-adjusting the factors. It's quite surprising how many different variations are possible within a single formula so don't discard it too quicky - you might miss on something. By adjusting the two knobs of the "Random Range" slider you can limit the numeric range of the random numbers that are used.

The "Randomize Vars" button will keep the formula and the numeric factors but switch around the x,y,width and height variables, this often just switches the orientation of the image but sometimes a simple stripe pattern becomes a complex texture.

If you manage to discover an interesting image please share it on formulizer.tumblr.com by clicking on the "Share on Tumblr" button. In case you come across something that looks like random noise I'd be very interested in that since those formulas can be very useful for procedural terrain generation or as a quick random number generator in shaders.

Since there is a daily limit of 75 uploads the submission might not be accepted, in that case you can copy the link and try again a few hours later.

The "Copy Link" button will copy a link to your current creation to the clipboard so you can share it with others.

Credits:
The idea for is based on my previous project nQbitor which again was based on ideas by viznut
nQbitor uses As3Eval by Metal Hurlant and the MinimalComps by Keith Peters