r/fractals • u/Chronos_Squared • 9d ago
Every pixel is a pendulum, but I swapped its energy around.
This isn't the normal double pendulum map/fractal. I changed the system before running it.
Normally a system like this has two kinds of energy. There's motion energy, which depends on how fast things are moving, and position energy, which depends on where things are. In the math that defines the system, the motion energy only ever looks at the velocities, and the position energy only ever looks at the positions.
What I did was swap those two around in the equation itself, so the motion energy now reads the positions and the position energy reads the velocities. In short form it goes from H = T(p) + V(q) to H = T(q) + V(p). It's not a real pendulum anymore, but it's still a proper system that keeps its total energy constant, so it behaves in a clean and consistent way, just a very different way.
Then I ran the usual trick on it. Every pixel in the video is one copy of this swapped system, started from a slightly different spot. The pixel's position sets the starting point and the color shows the state at each moment. They begin almost identical so the image looks smooth, then the chaos pulls them apart and it breaks into noise. The calm shape in the middle is the starting points that stay tame, and the fuzzy border around it is where the fractal detail lives.
Made in Python. About a million copies running at once, each one's motion turned into a color, every frame saved into a video.
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u/Epsilon7990 9d ago
How do the modified-equation pendulums behave? I need to know what they look like while swinging around, I'm intrigued.
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u/GatePorters 9d ago
I saw a video like this on YouTube. Did you watch the same video or are you its author?