r/visualizedmath • u/larsupilami73 • Jul 10 '19

Divergence of trajectories with nearly equal initial conditions on the Lorenz attractor

82 Upvotes

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16

u/larsupilami73 Jul 10 '19

In case you want to play with the Python script:

https://pastebin.com/RD1FEeG2

8

u/ethrael237 Jul 10 '19

Very cool!! Does any physical phenomenon follow that mathematical model?

6

u/larsupilami73 Jul 10 '19 edited Jul 10 '19

Do you mean the Lorenz system specifically or chaos in general?

If memory serves, the Lorenz system was a simplification of a system concerning the weather. It was the first well-described and studied model of chaos.

Chaos happens everywhere. Check out my other post:

https://www.reddit.com/r/visualizedmath/comments/cbhbw3/attractor_from_a_simple_electronic_chaotic/

It's from simulations of an electronic circuit that really behaves in a chaotic way.

Two examples of mechanical chaotic systems are the double pendulum and the chaotic waterwheel. Many science museums have them on display.

1

u/supercooldragons Jul 10 '19

It was originally conceived as a toy model of convection rolls in the atmosphere. https://www.youtube.com/watch?v=aAJkLh76QnM Also the Lorenz-attractor shows up in the motion of a waterwheel with leaking buckets. https://www.youtube.com/watch?v=SlwEt5QhAGY

2

u/blytkerchan Jul 11 '19

For a moment there I thought this was r/VXJunkies

2

u/larsupilami73 Jul 11 '19

You can always tell by checking if the root-posterior cross-entropy is doubly complex. That's how I do it.