#chaotic solutions

[magictransistor]

An assortment of computer models rendered employing variations of the Lorenz equation.

[the-entire-scalie-fandom]

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[the-entire-scalie-fandom]

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[magictransistor]

An example of a Lorenz attractor as described by a color computer model.

[jasper-rolls]

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G4M3-0V3R!!1 - Kobaryo [chaotic solutions]

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[iomikron]

This is an attractor of the Lorenz's dynamical system. This system has 4 parameters. Changing slightly the value of one parameter and maintaining the values of the others fixed, we can observe qualitative changes in the solutions of the system for all these different values. 

In this animation the orbit of each solution is displayed. For the first values of the parameter the dynamical system converges to periodic solutions. The period of the initial orbit increases for the increasing parameter's values going through a semi-periodic orbit and eventually to chaos.

Although the animation ends before a clear chaotic orbit emerges, in final frames you can watch in the background a part of the orbit, that forms the 'phantom' of chaotic orbit... This is a short route to chaos.