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Douady Rabbit
A Douady rabbit is a fractal derived from the filled Julia set, Julia set of the function f_c(z) = z^2+c, when Parameter (computer programming), parameter c is near the center of one of the Mandelbrot set#Main cardioid and period bulbs, period three bulbs of the Mandelbrot set for a complex quadratic map. It is named after France, French mathematician Adrien Douady. Background The Douady rabbit is generated by iterating the Mandelbrot set, Mandelbrot set map z_=z_n^2+c on the complex plane, where parameter c is fixed to lie in one of the two period three bulb off the main cardioid and z ranging over the plane. The resulting image can be colored by corresponding each pixel with a starting value z_0 and calculating the amount of iteration, iterations required before the value of z_n escapes a bounded region, after which it will diverge toward infinity. It can also be described using the ''Complex quadratic polynomial#Forms, logistic map form'' of the complex quadratic map, specific ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractal
In mathematics, a fractal is a Shape, geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine geometry, affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they Scaling (geometry), scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
