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About ChaosLab™ |
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Chaos theory and fractal geometry are two of the most important revolutions in scientific thought to have occurred in the twentieth century. Due to sheer computational demands, meaningful exploration could not begin until sufficient computing power emerged in the 1970s. Chaos theory deals with the idea that very simple non-linear dynamical systems can behave in very complicated, seemingly random, ways. Such systems exhibit what has become known as sensitivity on initial conditions. Small changes in a system's initial state give rise to unexpected outcomes. Can the flap of a butterfly's wings be responsible for a hurricane halfway around the world? Questions like this are at the heart of chaos. Fractal geometry is related to chaos theory in that many fractals are the result of non-linear dynamical systems. In 1918, the French mathematician Gaston Julia published one of the first papers on the subject. Among other things, the paper showed how the iteration of a function describing a very small part of the boundary of a mathematical object could regenerate the whole boundary. Julia's work pointed at one of the essential properties of fractals (and perhaps of nature): self-similarity at different scales. Liek chaos theory, fractal geometry is a new science that is already changing our fundamental assumptions about reality.  ChaosLab™ is an interactive math package that helps students visualize and understand fractal geometry and chaos theory. While generating and exploring their own fractal images, students encounter the core concepts in fractals and chaos. ChaosLab™ was designed for use in high school and college math courses.The software is made up of several interactive experiments that give rise to interesting mathematical questions. The experiments in ChaosLab™ were originally developed during the completion of Fractals In Your Future by Ron Lewis of Sudbury, Ontario. Fractals In Your Future is an instructional text and lab manual designed for use at the high school level. ChaosLab™ was initially intended to complement Fractals In Your Future; however, the software can be used on its own or in conjunction with another text. With ChaosLab™, students can now explore fractals and chaos using only their computer, Living Graph Paper™ and their imagination. |
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