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!
Full tutorial in GeoGebra classic:
https://youtu.be/8_BLhxjrho0
Video tutorial using GeoGegra Suite App:
https://youtu.be/L9qQFJnFmZQ
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
