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
Mountains of Fractals Launcher package.
An ready to run Launcher package containing the Mountains of Fractals Java programs. Download and then double click the Fractals.jar file to run the program… more... download 4969kb .jar
Last Modified: September 11, 2009
Chartier, T. (2008). Mountains of Fractals. Retrieved December 18, 2014, from http://mathdl.maa.org/jsp/search/searchResults.jsp?url=http://mathdl.maa.org/mathDL/4/?pa=content&sa=viewDocument&nodeId=1795
%0 Electronic Source %A Chartier, Tim %D 2008 %T Mountains of Fractals %V 2014 %N 18 December 2014 %9 application/java %U http://mathdl.maa.org/jsp/search/searchResults.jsp?url=http://mathdl.maa.org/mathDL/4/?pa=content&sa=viewDocument&nodeId=1795
Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.