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 Golden Rectangular Solid 1.0 (Downloads: 158)
Visualize 3D golden-rectangular-solid analagous to the 2D golden-rectangle One might wonder if there is a 3-dimensional golden-rectangular-solid that is analagous to the 2-dimensional golden-rectangle, which can be sub-divided recursively so that each left-over rectangular solid has the same proportions as the original rectangular solid. The 3D analogue to the 2D golden rectangle does indeed exist, and is depicted by this application....
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Automaton Laboratory 1.0 (Downloads: 182)
Visualize hierarchical planar curves, a superset of epicycloids and hypocycloids This application is a laboratory for the creation of automata. An automaton is a system of circles (actually planar coordinate systems) moving relative to one another in a hierarchical fashion. That is, every circle in the system except one will be rolling along the circumference of one other circle at every moment in time. Automata are a superset of the mathematical curves called epicycloids and hypocycloids. Automata might also be called compound cycloids....
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Automaton Lab 3D 1.0 (Downloads: 171)
Visualization of hierarchical 3-dimensional curves The automata which are modeled in this application are composed of a set of spheres whose size and axis are relative to one another, and where each sphere is rolling upon the surface of one other sphere in a fully deterministic pattern in space and in time. The paths through space taken by one or more points within each sphere can also be visualized as the automaton carries out is choreographed movements. This application is a laboratory for the synthesis of the a...
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Mnemonic Curve 1.0 (Downloads: 175)
A memory game illustrating concepts about sequential memory Mnemonic Curve is fundamentally a game. The object of the game is to remember and repeat a sequence of mouse-clicks within a group of circles. Mnemonic Curve demonstrates principles governing our ability to remember a sequence of choices....
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Cosmic Heart 1.0 (Downloads: 216)
Visualization of relationships between tetrahedron, cube, and dodecahedron This application demonstrates the curious relationships wherein a tetrahedron can be inscribed in a cube in two different ways and a cube can be inscribed in a dodecahedron in 5 different ways. It also demonstrates a kind of quantum fluctuation or beating as a heart does, in which the tetrahedron oscillates back and forth between the two positions in which it can be inscribed in the cube, and in which the cube oscillates randomly between the 5 positions in which it ...
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Prime Integer Observatory 1.0 (Downloads: 229)
Visualization of integer factorizations as a scrollable table This application illustrates the notion of an integer?s factors, and of the related property of integers called primeness, or primality. An integer is called prime if it is the product of only one distinct pair of integers. For example, 11 is prime because the only pair of integers whose product equals 11 is 1 and 11, as in 1*11 = 11 ....
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TilingKing Game 1.0 (Downloads: 215)
TilingKing is a strategy game of territorial control TilingKing is a strategy game of territorial control which combines characteristics of the game of Go, in which the objective is to control a larger territory on a tiled game board than your opponent, and the "connection" games (Hex, Y, Havannah, TwixT, PuNCT), in which the goal is to form a fully-connected chain of pieces linking opposite sides of a tiled board. It is most similar to the games like *Star and Cathedral in its game play but is not constrain...
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Phyllotaxis 1.0 (Downloads: 183)
Visualization of phyllotaxic arrangement of circles Phyllotaxis is the study of the successive arrangement of radial parts of a growing plant, such as the leaves on a stem, or the seeds in the head of a sunflower. This application generates a simple phyllotaxic arrangement of circles, expanding outward at either a linear or an exponential rate. You can specify the angle between each circle (between 0 and 360 degrees), and you can determine rate of expansion using a pair of slider controls....
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