These are pretty great, Jason. Does it look interesting for the particles to leave shorter trails, or does it make it hard to appreciate the resulting pattern?
That's good insight, Vince. I suspect it will look nicer when shorter. They started very long, and I continually shortened them. But I didn't go shorter until I felt it was too far -- so I will try that in the next video.
Glad you enjoyed it. I think it's the easiest example to consider. Once you grok that, you can start to consider more complex examples. I still think the butterfly example is far fetched, since it requires many, many "just at the edge of impact" cases -- like those comedy movies where one funny act leads to another, leading to another -- all of which are "winning the lottery" chances.
A reasonable complex case is our Solar System: the planets are chaotic. It's not clear that some of them, and some of the moons, including our own, may be ejected from the Solar System even before the Sun runs out of energy. It's only known to be stable for at least 100 million years -- but not necessarily for the remaining 5 billion of the Sun's life.
I'd like to also show what happens if the particles start in any area of the 3D cube -- though it may be harder to view. The parameters themselves - sigma, rho, beta - could change, which may be interesting to explore.
🤯
These are pretty great, Jason. Does it look interesting for the particles to leave shorter trails, or does it make it hard to appreciate the resulting pattern?
That's good insight, Vince. I suspect it will look nicer when shorter. They started very long, and I continually shortened them. But I didn't go shorter until I felt it was too far -- so I will try that in the next video.
thank you for the asteroid example, really put the idea into perspective, crazy!
Glad you enjoyed it. I think it's the easiest example to consider. Once you grok that, you can start to consider more complex examples. I still think the butterfly example is far fetched, since it requires many, many "just at the edge of impact" cases -- like those comedy movies where one funny act leads to another, leading to another -- all of which are "winning the lottery" chances.
A reasonable complex case is our Solar System: the planets are chaotic. It's not clear that some of them, and some of the moons, including our own, may be ejected from the Solar System even before the Sun runs out of energy. It's only known to be stable for at least 100 million years -- but not necessarily for the remaining 5 billion of the Sun's life.
Very cool demonstration.
Thanks! I have lots more ways to show off these strange attractors... I have to figure out what would be best for visualization and interest.
Very very cool visualization.
I will try another one with shorter particle lengths. I could probably show more particles and have it still be readable.
I'd like to also show what happens if the particles start in any area of the 3D cube -- though it may be harder to view. The parameters themselves - sigma, rho, beta - could change, which may be interesting to explore.
❤