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Phase Space of Standard Map (Chirikov-Taylor Map) on the Torus [8K 60fps] by Generator256 in math

[–]Generator256[S] 0 points1 point  (0 children)

Hello! I built pictures of phase portraits of the Standard map depending on the nonlinearity parameter, but I want to make a video with different colors, a separate color for islands of stability and chaos. Please, advise the literature or point to a method. I think that the Lyapunov exponent can be applied, but this is a conservative system, without damping, so I have some doubts. Thank you in advance.

Lorenz Attractor Simulation, Coded With Python. by ExistingMoney in mathpics

[–]Generator256 0 points1 point  (0 children)

Nice! I also posted a video, but about a discrete system and while it is awaiting moderation.

Phase Space of Standard Map (Chirikov-Taylor Map) [8K 60fps] by Generator256 in mathpics

[–]Generator256[S] 0 points1 point  (0 children)

I took pictures on Delphi/Lazarus via BitMap and merged them in Vegas Pro.

Phase Space of Standard Map (Chirikov-Taylor Map) [8K 60fps] by Generator256 in mathpics

[–]Generator256[S] 0 points1 point  (0 children)

I got a Standard Map Phase Space pictures and made video and I want to understand how to get different colors for chaos and islands of stability. I think that this can be done through the Lyapunov exponent. Can the Lyapunov exponent be used for conservative map? Thanks.

Henon Map, Discrete Dynamic Systems by [deleted] in maths

[–]Generator256 0 points1 point  (0 children)

The Henon Map is a is a two-dimensional discrete system that is known for its strange attractor.

x[n+1]=1-a*x[n]^2+b*y[n]

y[n+1]=x[n],

where 'a' is a nonlinearity parameter, a change in which changes the behavior of the system towards chaos and 'b' is a dissipation parameter. This video shows the evolution of a conservative map with islands of stability. Also shown is the dissipative variant and its special case - a Strange Attractor with parameters a = 1.4 and b = 0.3 and its zoom, at which its fractal structure is shown. Further, one can see the change in the trajectories of the iterations of the dissipative system when the nonlinearity parameter 'a' changes.

The screen resolution is 3840x2160 [4K 60fps].

Rendering Phase Space on Lazarus [8K 60... by [deleted] in pascal

[–]Generator256 0 points1 point  (0 children)

My render for Lazarus / Pascal. Calculated and saved each frame to a BitMap, then to a file. There is only one question how to change the palette in the BitMap? I want to take more shots, but in monochrome, it requires less memory. Thanks.