Aesthetics II — Mathematical Art Some forms of Art are mathematically based. Take, for example, fractals, a part of the larger discipline of the mathematics of Chaos. The mathematical word "Chaos" does not mean anarchy or total craziness! It is a branch of mathematics that studies changing systems which are very sensitive to initial conditions. For example, the weather is described by chaos, and so is the meandering of rivers and crinkly shorelines. The images on the next page were made by using fractal equations. Click on this picture to see them ==> Here are some discussion questions you might want to think about ==> ? Another kind of mathematical art can be found in the discipline of Topology, the study of surfaces—many of them weird surfaces! Topology is sometimes called "rubber sheet geometry" since it deals with stretching surfaces of figures to turn them into other shapes. For example, according to topology, a doughnut and a coffee cup with saucer is the same figure, meaning if a doughnut had the pliancy of a rubber sheet, you could turn it into a cup and saucer without tearing an edge! This branch of mathematics also concerns knots. Take a look ==> (Bet you'll never look at knots in your shoelaces in the same way again....) Many of the drawings of artist Escher are based on mathematical imagery, shapes that transform smoothgly into other, often opposite, images. See, for example ==> Topology also deals with 3-dimensional objects that have only one side! The simplest of these is called a Mobius (pronounced moh-bee-us) Strip. One of Escher's drawings shows ants crawling along one: This strip has only one side! You can easily make a Mobius strip and prove it for yourself! Click on the ants above to get directions on how to make a Mobius strip and experiment with a one-sided piece of paper. Here are some discussion questions you might want to think about ==> ? Well, that's all, folks, except for a reading list if you want to read more and a list of some of my favorite quotations about mathematics and physics. And you have to see that poem I mentioned earlier! I hope you learned some new things and most of all, that you have a new perspective on the connectedness and beauty of Nature.