How to plot strange attractors

Description

With the following GeoGebra script you can plot the numerical solution of systems of differential equations. The main command used here is NSolveODE(). More info: https://wiki.geogebra.org/en/NSolveODE_Command Other Auxiliary commands used are: https://wiki.geogebra.org/en/Sequence_Command https://wiki.geogebra.org/en/Point_Command https://wiki.geogebra.org/en/Polyline_Command The 3D graphics view must be opened!

GeoGebra script

##Parameters## d = 10 b = 8/3 p = 28 ##System of differential equations: Lorenz attractor## x'(t,x,y,z) = d * (y - x) y'(t,x,y,z) = x * (p - z) - y z'(t,x,y,z) = x * y - b * z ##Initial Condition## x0 = 1 y0 = 1 z0 = 1 ##Numerical solution## NSolveODE({x', y', z'}, 0, {x0, y0, z0}, 20) ##Note## # The command NSolveODE() creates three curves # containing the numerical silution of the system # per variable (x,y and z) and they are plotted # against time in the 2D graphic view. ##Calculate length of solution 1## len = Length(numericalIntegral1) ##Define points from the solution## L_1 = Sequence( (y(Point(numericalIntegral1, i)), y(Point(numericalIntegral2, i)), y(Point(numericalIntegral3, i))), i, 0, 1, 1 / len ) ##Draw curve## f = Polyline(L_1) ##Finally, you need to hide numericalIntegra1, numericalIntegra2, numericalIntegra3, and L_1##

Result

Result

Short tutorial in the GeoGebra suite app

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