Alexander Gustafsson

Пікірлер

@PAND4.247 23 сағат бұрын

W A Y N E H Y L I C S

@unexpectedTrajectory Күн бұрын

Took me a while to realize what was going on. Once I realized , it was one of the most beautiful things I've ever seen :)

@dougrutledge532 2 күн бұрын

okay, now add collisions between the balls ;P

@eugenetheant 2 күн бұрын

Can't agree with the "Classical" part. In your simulation particle (a ball) doesnt change it's direction after it collides with edge of the slit. And so there is nothing special in such a result of this "classical" simulation. Dislike

@sierpinskicarpettothepowerof4 4 күн бұрын

The title don’t have anything wrong lol

@sierpinskicarpettothepowerof4 4 күн бұрын

Cause balls isn’t a swear word

@JokerGaming-iv1tm 5 күн бұрын

Satisfying

@ORGOrange 5 күн бұрын

(moose noises) (turns into a black hole)

@ORGOrange 5 күн бұрын

moose

@truongquangduylop33yyuh34 9 күн бұрын

behold da moose nebula

@theftmoxi5 10 күн бұрын

Feels like a scientific* film in 1975

@lemonize30 10 күн бұрын

Shoutout all my hyperboles

@lucaballer 11 күн бұрын

How many balls

@kaystephan2610 13 күн бұрын

Me: "Today's gonne be a crazy productive day" KZfaq: gravitational collapse of a moose Me: 👀

@TheUltimateRare 15 күн бұрын

100 balls reminds me of fireworks going off.

@user-jq2im1mv6f7 15 күн бұрын

They suddenly increased

@iamanevutable981 16 күн бұрын

If they're both intangible to each other and identical, wouldn't they by definition be moving together existing as one ball?

@animations_ag 16 күн бұрын

The balls are separated by a small distance. The chaotic system means that the distance between the balls increase exponentially, which becomes very apparent eventually.

@catmacopter8545 18 күн бұрын

How did you interpolate between the different iterations to make the "ink" effect?

@sofia.eris.bauhaus 17 күн бұрын

there is a formula for "smooth" mandelbrot renders, but i don't really get how it works 😅.

@animations_ag 16 күн бұрын

I used a logarithmic falloff, sort of. That is, the region between the steps constitutes additional decaying steps. This was the python function used: def mandelbrot_set(xmin, xmax, ymin, ymax, width, height, max_iterations): x = np.linspace(xmin, xmax, width) y = np.linspace(ymin, ymax, height) X, Y = np.meshgrid(x, y) C = X + Y * 1j Z = np.zeros_like(C, dtype=np.complex128) div_time = np.full(C.shape, max_iterations, dtype=float) for i in range(max_iterations): mask = np.abs(Z) <= 2 Z[mask] = Z[mask]**2 + C[mask] mask_diverged = np.abs(Z) > 2 # Only update div_time where it hasn't been updated yet (was max_iterations) div_time[mask_diverged & (div_time == max_iterations)] = i - np.log(np.log(np.abs(Z[mask_diverged & (div_time == max_iterations)]) + 1e-10)) / np.log(2) return div_time See also: en.wikipedia.org/wiki/Plotting_algorithms_for_the_Mandelbrot_set

@wallabra 18 күн бұрын

So cool! I love this kind of visualization. Anyway, can't a logarithmic/exponential falloff be used to be able to 'liquefy' the iterations continuously, rather than doing the animation in segments?

@animations_ag 16 күн бұрын

Yes, that's basically what I did. This was the function used (see last line of the function, especially): def mandelbrot_set(xmin, xmax, ymin, ymax, width, height, max_iterations): x = np.linspace(xmin, xmax, width) y = np.linspace(ymin, ymax, height) X, Y = np.meshgrid(x, y) C = X + Y * 1j Z = np.zeros_like(C, dtype=np.complex128) div_time = np.full(C.shape, max_iterations, dtype=float) for i in range(max_iterations): mask = np.abs(Z) <= 2 Z[mask] = Z[mask]**2 + C[mask] mask_diverged = np.abs(Z) > 2 # Only update div_time where it hasn't been updated yet (was max_iterations) div_time[mask_diverged & (div_time == max_iterations)] = i - np.log(np.log(np.abs(Z[mask_diverged & (div_time == max_iterations)]) + 1e-10)) / np.log(2) return div_time

@krispy_kornflake 18 күн бұрын

when you're tripping so hard the ink spills into perfect mandelbrot set

@sofia.eris.bauhaus 18 күн бұрын

that's a very cool to visualize it! would be nice to see it iterating and zooming at once, but maybe that presents some timing difficulties 😅.

@animations_ag 16 күн бұрын

Yes, that timing :). Have elaborated a bit with that recently; can't find a robust relation between zoom level and number of iterations. It appears also depend on the zoom coordinate, i.e., different relationships for different boundary coordinates.

@sofia.eris.bauhaus 15 күн бұрын

@@animations_ag ah, that makes sense, actually. after all, different iteration depth reaching different places is the very thing the mandelbrot fractal shows. well, it also should be more complex than a julia fractal in this regard 🤔.

@cheeseboy8241 18 күн бұрын

very well crafted. that's one of my favorite parameters to play with visually and this felt like a culmination of what I've been dancing around

@grabs_you5954 18 күн бұрын

Love this music and I love fractals

@adamusher5294 18 күн бұрын

That was really cool! From around the 14 second I was perceiving the black as the "negative space", then at the one minute mark my worldview was dismantled in an instant as the true nature of reality became clear. Great stuff!

@Armund_Wolffe 18 күн бұрын

gorgeous! i could watch these for hours.

@BigParadox 18 күн бұрын

For me, that was a somewhat new way of looking at fractals. Very cool!

@animations_ag 18 күн бұрын

Full song: kzfaq.info/get/bejne/fbOJi6xknrO9f4k.html Visuals inspired by: kzfaq.info/get/bejne/pqpnktFmzKm5gH0.html

@error_6o6 22 күн бұрын

This is why you do not drop a moose onto this curve.

@error_6o6 22 күн бұрын

Oh, so now we’re upgrading to triples. Was kinda waiting for that to happen.

@DcorneaterYT 23 күн бұрын

0:06 The Line Synced With The Music,Witch Makes The Video More Comforting

@christijamelle 26 күн бұрын

0:31

@huseyinatak1003 27 күн бұрын

I found so much in your work (maybe because I'm high most of the time but also I'm a decent mathematician + architect) yet you are so unknown... It feels like I'm blessed getting to witness these. Thank you Alexander Gustafsson

@animations_ag 26 күн бұрын

Wow, thanks a lot!

@Yunahsky Ай бұрын

Brain nourishment.

@salvulcanogaming Ай бұрын

did you change your pfp?

@animations_ag Ай бұрын

Yes :)

@Slugcat770 Ай бұрын

Wdym by cute bug? Wheres the bug? Is this clickbait?

@animations_ag Ай бұрын

At 1:34 and 1:47.

@momom6197 Ай бұрын

A few questions for the mathematically inclined: - Is the triple pendulum in some sense more chaotic than the double pendulum? In what sense? - If you replace the pendulums by distributions (to simulate an infinity of them), what does the density look like over time?

@Zymplectic 22 күн бұрын

- Yes, in the sense that it has more degrees of freedom allowing it to be hyperchaotic, which has various implications such as multiple positive Lyapunov exponents: It is potentially more chaotic in terms of dimensionality. - The system is Hamiltonian and abides by ergodic theory / Liouville's theorem, and so any of the triple pendulums with the same energy will fill the same phase space. Practically speaking, if you try to map the average location of the outer pendulum bob for each pendulum, the map from each pendulum would be become indistinguishable when averaged over long time scales.