Some pretty pictures drawn with math for you to enjoy on this Sunday. I'll post the equations I used in Javascript for you to go along with the picture. The one at the top is one I did a few weeks ago, and I can't really remember the equation for it.

The first one is a simple spiral. I'm calling it "Ripples on a pond" because that's what it looks like to me. It's an Archimedes Sprial with a parametric equation of x = (3 + 4 * theta) * Cos(theta), y = (1 * theta) * sin(theta), where theta is a series of numbers between 0 and 720 that increases by 0.01. This is giving me a magic eye vibe, honestly. It might be my screen resolution, but I think I can see a bend in the shape o an hour glass on it.

It would be fun to discuss random patterns within finite possibilites. These pictures are probably nothing new, since they use every day fomulas to make. What makes the pictures fun to make is cranking up the number of lines and seeing what kind of patterns emerge. My computer is a constantly disappointing pile of crap. For whatever reason I can't do a really high count. So enjoy these pictures as something to look at, and enjoy your Sunday.

This looks like an eyeball, right? If you trace the lines, you can see the reflections of light. Uses the parametric eqaution of a circle x = 200 * cos(theta), y = 200 * sin(theta), theta is the tangent of a series that increases by 1.

I used to have fun with things like this. The hourglass shape in the spiral looks like a variation on Moiree patterns. You can see these by drawing straight lines from a central point to evenly-spaced points on the perimeter of a rectangle. They come about because of the pixel resolution in drawing a diagonal line or curve - where it steps sideways as it goes - and the alignment of these steps between closely-spaced adjacent lines.

ReplyDeleteThanks for the explanation! I knew it had something to do with the resolution, but I wasn't sure if it was the screen or the picture. I've been havig so much fun with these patterns I wanted to share.

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