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An attractor is a set of states for a dynamical system towards which arbitrary states tend to evolve; attractors are called ‘strange’ when they exhibit fractal-like behavior.
This program visualizes several three dimensional dynamical systems with strange attractors, accessible via the menu in the top right. The defining differential equations are below:
The aizawa attractor arises from the following dynamical system with parameters $a=0.95$, $b=0.7$, $c=0.6$, $d=3.5$, $e=0.25$ and $f=0.1$.
$$ x^\prime = (z-b)x-dy $$$$ y^\prime = dx+(z-b)y $$$$ z^\prime = c+az-\frac{z^3}{3}-(x^2+y^2)(1+ez)+fzx^3 $$The Chen attractor arises from the following dynamical system with parameters $a=5$, $b=-10$, and $d=0.38$.
$$ x^\prime = ax-yz $$$$ y^\prime = by+xz $$$$ z^\prime = dz+xy/3 $$The Dadras attractor arises from the following dynamical system with parameters $a=3$, $b=2.7$, $c=1.7$, $d=2$ and $e=9$.
$$ x^\prime = ax-yz $$$$ y^\prime = by+xz $$$$ z^\prime = dz+xy/3 $$The Rossler attractor arises from the following dynamical system with parameters $a=b=0.2$ and $c=5.7$.
$$ x^\prime = -(y+z) $$$$ y^\prime = x+ay $$$$ z^\prime = b+z(x-c) $$The Sprott attractor arises from the following dynamical system with parameters $a=2.07$ and $b=1.79$.
$$ x^\prime = y+axy+z $$$$ y^\prime = -bx^2+yz $$$$ z^\prime = x-(x^2+y^2) $$The Thomas attractor arises from the following dynamical system with parameter $b=0.208186$
$$ x^\prime = \sin(y)-bx $$$$ y^\prime = \sin(z)-by $$$$ z^\prime = \sin(x)-bz $$