Mathematical Constructs

It's no secret that I love math. I think if I had to go back and choose a different major in college it would have been mathematics. Over my Christmas vacation I had an old issue of Dell's Math and Logic problems that I worked on in quiet moments. The 'artsy' type however is not known for her or her skill in mathematics. But without a little mathematics background it may be difficult to draw inspiration from: z^3 - z^2 + c.

Yes it is true that I do enjoy puzzle books, especially those dealing with logic and math problems. I do not get every problem right, but I do have a better than average record in successfully and correctly completing the problems. My odd interest however garners funny looks from many people including my wife. In many people's opinion, "Why would I want to put myself through that kind of torture?!"

But the truth is, it is relaxing to me. I like to look for the patterns and the exact answers that come from solving the problems outright. Two plus two will always be four in elementary mathematics. And it is from the more complicated problems that have a multitude of solutions, like the one I put above, that produce interesting patterns and if twisted and turned produce interesting art.

Using the idea above I started to use POV-Ray to generate a range of value to plug into the equation. In a straight forward fashion I just assigned values to the x, y, and z coordinates of a sphere. Where that sphere fell in space was left up to combinations like z times z times z and -z times z. While that may not make a whole lot of sense to some of you, it's like placing a ball 3 feet straight into a room and turning and moving it another 3 feet. It's like positioning Styrofoam balls where planets might be in various places inside of a room. The difference is I'm following a formula based off a fractal.

It's really quite easy to take this idea of a range of numbers and creating an image. It takes very little knowledge of the programming environment, however it does take a minimal amount of programming. Which is anyone requests it I can put the text of the program I wrote in a small document o copy and paste and play with yourself.

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