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Bifurcation Diagram Math-Chaos Theory |
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![[Bifurcation Screenshot]](gfx/shots/bifurc.gif)
This program draws the bifurcation diagram for Verhulst's model of
restricted population growth, which is based on the simple equation:
xn+1 = axn(1 - xn).This stuff is really
fascinating! For instance, this is where the universal constant,
Feigenbaum's number, is easily manifested (it occurs in the recurrence of
the period doubling).
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Fractal Explorer Math-Fractals |
Fractal Explorer is a program that let's you explore fractals especially those that are drawn as recursive curves. You'll find here the Dragon curve, the Koch curve, the Fern, Sierpinski Gasket, and two other curves of my own making.
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Lightning and Tree Generator Math-Fractals |
These are variant programs of the same algorithm that draws realistic looking lightning and trees. They are drawn using a fractal growth process. You can change certain variables to adjust specific settings.
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Boolean 1D Cellular Automata Math-Artificial Life |
![[Cellular Automata Screenshot]](gfx/shots/automata.gif)
This program generates a 1D cellular automata except that it isn't binary
(i.e., the cells don't have a value of 0 or 1). Here, any cell can take on
values from 0 to 255. And the rules governing the development of the next
generation uses Boolean logic.
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Rosette Math-Geometry |
This program draws a Rosette pattern which is just a regular polygon with all the diagonals drawn in. The program can be turned into an alternate screen saver where you can see shifting iridescent colors as the program draws a high-order rosette pattern.
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Triangle Math-Geometry |
Triangle is a geometry program that draws a triangle and displays some of its special properties such as altitudes, perpendicular bisectors, incircle, Euler line, etc. I might update this to add more properties and to make it more interactive.
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