Mathematical Curiosities

Last Updated 10/9/99



This applet provides a geometric introduction to fractals by illustrating how simple fractals are generated using initiators and generators. It features class fractals such as the Koch curve, the Sierpinski gasket, the Dragon curve and more. In addition, the applet also includes original fractals such as the Dragon leaf and variations on the Sierpinski carpet. (1/19/99)

Use this applet, an extension of the fractal applet above, to create your own fractals. Still under development. (8/8/99)
Uses JDK 1.2.

Mandelbrot Viewer
Fractals such as the Mandelbrot Set and its Julia Sets are generated by interating a function and checking for convergence, and this applet is mainly an exploration of fractals generated using that method. So in addition to the Mandlebrot set, the applet also features the Sierpinski Triangle and other fractals generated using an iterative approach. (1/31/99 - Last updated 8/8/99)

Spinning Spirals
While not true fractals, the patterns generated by this applet are truly stunning, reminiscent of giant blossoms or the intricate patterns of stain glass windows. (1/17/99)

Pythagorean Trees
Pythagorean trees are created by starting with a square, attaching a right triangle to one of its sides, attaching two squares along the free sides of the triangle, and repeating ad infinitum. (1/16/99)

Conways's Game of Life
This applet illustrates the Game of Life, a cellular automaton discovered by the mathematician John Conway. The Game of Life demostrates how complex behavior can emerge from extremely simple rules. (8/10/99)

Lorenz Attractor
Simulation of the Lorenz Attractor, one of the first systems in which chaos was observed. The Lorenz system is a model of thermal convection that emerged from the study of equations used in the prediction of weather. (9/12/99)

Bifurcations NEW (8/29/03)
Bifurcation Applet.

Math/CS Problems

Graph Sort
Graphical demonstration of several different sorting algorithms. Among the sorting algorithms shown are quicksort, selection sort, merge sort. (4/19/99)

Traveling Salesman
Explore the classic problem of the Traveling Salesman. The salesman has to stop at n cities, and he wishes to take a tour so that he visits each city exactly once and finishes at the city that he started from. This applet is a demostration of one possible algorithm he can use to minimize the total cost of the trip. (8/2/99)

Buffon's Needle
A simulation of the problem of the Buffon's Needle, a probabilistic method for estimating pi by throwing a needle onto a grid of parallel lines. (10/9/99)

Bending Bridge
A simulation of how the number of modes affects the response of a bridge. (10/9/99)

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