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written by Tim Chartier
The "Mountains of Fractals" article in the Math DL develops algorithms to produce coastlines and mountains in two dimensions by adapting mathematical ideas related to the construction of such fractals as Koch's curve. EJS is used to create a hands-on activity that allows a reader to create a coastline with a rubberband, six-sided die, and thumb tacks. Java applications allow for exploration of these algorithms and the influence of their associated parameters. After discussing 2D fractal mountains, this article extends the 2D algorithm to produce 3D mountains. Finally, mathematical issues in random number generation are discussed. More specifically, linear congruential generators are considered and shown to be suitable as a random number generator for the 3D fractal landscape algorithm. The use of fractal landscapes in movies is also discussed.
Please note that this resource requires at least version 1.5 of Java (JRE).
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