Geometry based imaging provides attractive sceneries with perfect mathematical forms provided by its infinite scaling capability and the precise changeability of object shapes. If mathematical numeric control meets the artist's creative manner, this brings a powerful image generator to the studio. I have been using geometric objects, mostly the surfaces of hyperbolic paraboloid for the images in Geometrica.

In the meanwhile, a method absolutely free from the geometric parameter manipulation is possible with processing stochastic elements. Like the technique of pendulum in photography, while its production rate of acceptable result is very low, its potential of generating a strong visual message is also very attractive. Each image in Stochastica was rendered with some hundred light source data generated by a stochastic process.

In math controlled creation, the abundance of options available to the artists can easily lead them to go astray in the maze of parameters. When you want to control the parameters by an algorithm, you must face a difficulty in tuning the color or the shape since they are affected by each other. In my case, as works are always the results of one time calculation, designing adequate algorithm for the motif is the most important and time-consuming job.

No matter how you use a computer, or whichever computer you use, to create an art work is not easy. Nevertheless, I believe artists can find a new horizon in his/her creative activities by having the experience of using geometric object and/or stochastic process. For artists who want to create mathematical art through algorithm-driven parameter control, the essential element for success is artistic serendipity. This is the interesting fact of art in the perfect mathematical space. - Y. Abe