Lorentz
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Description: The "Lorenz Attractor" is a "simple" set of three deterministic equations developed by Edward Lorenz while studying the non- repeatability of weather patterns. The weather forecaster's basic problem is that even very tiny changes in initial patterns ("the beating of a butterfly's wings" - the official term is "sensitive dependence on initial conditions") eventually reduces the best weather forecast to rubble.
The lorenz attractor is the plot of the orbit of a dynamic system consisting of three first order non-linear differential equations. The solution to the
differential equation is vector-valued function of one variable. If you think of the variable as time, the solution traces an orbit. The orbit is made up of two spirals at an angle to each other in three dimensions. The equations are:
dx/dt = -a*x + a*y
dy/dt = b*x - y - z*x
dz/dt = -c*z + x*y
default values are time step = .02 ,a = 5, b = 15, c = 1
Different Lorenz attractors can be created using different parameters. Four parameters are used. The first is the time-step. The default value is .02. A smaller value makes the plotting go slower; a larger value is faster but rougher. A line is drawn to connect successive orbit values. The 2nd, third, and fourth parameters are coefficients used in the differential equation (a, b, and c). The default values are 5, 15, and 1. Try changing these a little at a time to see the result.
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