ubikuberalles' Blog - The Equations program (Art via Programming)

[RSS Bot]

In my previous "Art via Programming" <url="http://ubikuberalles.livejournal.com/45159.html"]blog entry[/url], I talked about the Circles program which generated pretty pictures via the "X^2 + Y^2" equation. I added different equations to get different results and before long it was pointless to call the program "Circles". Therefore, I archived the original Circles program and created a new program called "Equations". The current version of Equations can plot up to 15 different equations that I either dreamed up myself or were suggested by my readers (Thanks supercat!).

 

Here's what Equations looks like with the |acos(x) + acos(y)| equation:

 

 

Notice that the controls for the program are different. The x-min,x-max,y-min and y-max controls allow you to zoom in or out of a particular region of the equation space. The "delta" control allows you to increase the power setting in increments 0.01, 0.1, 1 or 10 (or you could just type in the power level you want but that means taking your hand off the mouse).

 

Here's the result of the lnx * lny function:

 

 

The tanx + tany function:

 

And the X^3 + Y^3 function:

 

 

I also made some movies from the program:

 

atan(x) + atan(y) - medium (200 X 200 - 1.03 MB)

atan(x) + atan(y) - small (150 X 150 - 502 KB)

 

tan(x) + tan(y) - medium (200 X 200 - 1.2 MB)

tan(x) + tan(y) - small (150 X 150 - 593 KB)

 

X + Y - medium (200 X 200 - 459 KB)

X + Y - medium (150 X 150 - 332 KB)

 

If you want to check it out, you can run the Equations program yourself since it is a Flash program. Click here to run the program. As, I said there are 15 equations to play with and, with the zoom controls, you can explore different regions of the patterns generated. Be warned that this program is CPU intensive and, depending on the power of your computer, may take a few minutes to complete (it takes about 15 seconds with my 1.6 GHz Sempron).

 

The color schemes of the patterns, as you can see, are all very similar. That's because I simply mapped the output value of the equation into the 24 bit color map. In a future program I may consider going back to using a palette like I did with the patterns program (in fact I'm considering creating a palette version of the Equations program to see if the results will change).

 

This was an interesting program and I learned a lot about Actionscript and the combo boxes. However, I think I hit my limit with this equation approach and it's time to move onto something with more variety in the patterns. In other words, it's time to look at non-linear or chaotic equations (Julia sets, Mandelbrot, etc.).

 

Before I do that, however, I decided to revisit my patterns program with some ideas and that's what I'm going to talk about next.

 

http://www.atariage.com/forums/index.php?a...;showentry=3243