Alexander Gustafsson
Oxidized copper wire moose drawn by 30 000 Fourier harmonics
updated
Music by @gpcbass - this cool song is called "Here it is".
Visuals in Mathematica.
The song, Imperial March by John Williams, is here reproduced by @PowerofPenguin (my son, playing the bass) and @gpcbass who made some adjustments to a premade version of the song. Bass playing by Julius in action can be seen here: youtube.com/watch?v=No0wjSw0T9c
Visuals in Python and FFmpeg
Music by @gpcbass. The song, made yesterday, is called Dance Floor.
Visuals in Mathematica.
A spherical shell with homogeneous mass distribution obeys the same Newtonian gravitational force as if all the mass was centered in the sphere. Close to the surface, normal projectile (parabolic) motion can be observed as we see close to Earth's surface. However, inside the shell the gravitational force exactly vanishes. That is, if earth would be hollow, then upon drilling a hole on the surface, we would experience normal gravity on the outside and zero gravity if daring jumping down the hole.
The sphere is here depicted in two dimensions for visual purposes. Further, the effect of the hole is ignored, i.e., the ball moves as if there was a shell where the hole is placed.
More info of this concept here: http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/sphshell2.html
Beautiful music by @gpcbass and Rogge. It's a Bach reproduction. Full version and more info here: youtube.com/watch?v=1LUzDOIIFO0
Visuals in Mathematica
The only interesting part, in my opinion, is the Anderson localization clearly seen in the final random lattice, as expected for such a "lattice".
Music by @gpcbass. The song is called Gitter Cat.
Visuals in Python and FFmpeg.
Left: A very simple maze that an reinforcement, RL, learning agent improves its ability to find the fastest way between start (upper left) and goal (lower right) utilizing a grid-based Q-learning simulation.
Right: The number of steps the agent takes in each episode.
The excellent song is a reuse from a previous video, made by @gpcbass. It's called Swing Zero.
Video compression is significant, and the visual quality is crap regardless of video rendering settings.
The song, Swing Zero was made @gpcbass.
Visuals done in Mathematica.
Simulation was done in Mathematica, i.e., analytically computed reflections. The initial configuration of the particles is normally distributed with similar parameters as in the quantum version.
The quantum and classical solutions are very similar, and I tried blending both animations by fading back and forth between them in the same video, which unfortunately "screwed up the bitrate" badly when uploaded on YT - hence they are separated in two videos.
The beautiful song is made by Dennie a.k.a. @gpcbass (keys and bass) and Rogge (guitar). The song can be listened to/viewed in its entirety here: youtube.com/watch?v=GMYXI39MYOU. This song is a remake of J. S. Bach's Preludium BWV935.
The caustics are interesting, and are (I guess) cardioids of various sizes.
The discrete domain has dimensions 2160x2160 (4k), and the 7200 frames took approx 6 hours to generate on a MacBook Pro M3 Max.
Music made by @gpcbass today, called Fourth Note.
Visuals in Python and FFmpeg.
The beautiful song is made by Dennie a.k.a. @gpcbass (keys and bass) and Rogge (guitar). The song can be listened to/viewed in its entirety here: youtube.com/watch?v=GMYXI39MYOU. This song is a remake of J. S. Bach's Preludium BWV935.
Video frames made in Python and stitched in FFmpeg.
Visuals inspired by youtube.com/watch?v=pD7_n5gCUPI (their transitions are better, though).
SymPy was used to determine the equations of motions of the triple pendulum.
The song was made by @gpcbass a couple of years ago, called "Fjäriln vingad" (originally made by C. M. Bellman centuries ago).
Visuals in Python & FFmpeg.
Music: @gpcbass; song called Minor Step
A MWE softbody code can be found on my git.
Music made yesterday by @gpcbass. Song is called Ancient Jumper.
Visuals in Python & FFmpeg.
Music by @gpcbass. It's a remake of Joni Mitchells song Both Sides Now from 1966. Retrobites (gpcbass' band) version can be enjoyed here: youtube.com/watch?v=ChBU3O9MxAQ
The bug in this system will never be resolved. Here a single annoying ball suddenly decides to take a strange non-physical path.
Music: Prime Time by @gpcbass. Used before here.
Visuals in Python and FFmpeg.
This time it continues with 5000 randomly distributed point masses confined to the interior of a moose-shaped contour, the points being released under gravity and falling on the function f(x) = abs(x). This is a non-chaotic system but the points spread out linearly over time and eventually reveals a shockingly nimble moose.
The bug in this system still bugs me. On rare events a ball or two decide to take a non-physical path.
Music: Gravity_Y by @gpcbass. Used before here.
Visuals in Python and FFmpeg.
The Barnes-Hut approximation method is used. Developed with help of chatGPT.
Music made by @gpcbass today; the song is called Minor Step.
Visuals in Python and FFmpeg.
Image acquisition was done with ZWO's AM5 mount and ASI2600MC PRO camera through a Skywatcher 100ED DS-PRO refractor with a .85 reducer, i.e., at 765 mm focal length and f/7.65. Taken from a Bortle 4 zone.
In total 80 5-minute exposures (6 hours and 20 minutes). Stacking, edge cropping and background extraction was made in Siril, and the remaining postprocessing in PixInsight. Particularly, the magic wands Blur- and Noise exterminator were used therein. I spend typically 30 minutes on post and have much to learn as some may notice.
No affiliation involved.
Astrophoto channels I like:
@NebulaPhotos Nico is brilliant on what he does and is the main reason that I eventually went into astrophoto two years ago (with a DSLR and a tripod).
@lukomatico Superb in-depth comparisons among gears, and always provide interesting tutorials and reviews.
@CuivTheLazyGeek Enthusiastic and entertaining reviews/comparisons/tutorials. Always a pleasure to watch.
Visuals made with my astro camera and telescope; images stitched and blended in ffmpeg, as well as some Python tweaks.
The beautiful music was made by @gpcbass; the song title is Starless (a King Crimson cover from 2022). A vocal version can be found here: youtube.com/watch?v=TbJvKYycOAY&ab_channel=gpcbass
The balls in the superellipse display a chaotic behaviour compared to the linear case for the ellipse.
Music by @gpcbass. The song is called End of nine 2, and made today specifically for this video.
Visuals done in Python and FFmpeg.
See github.com/alguaa/animations_ag for source code. I spent some extra time to make the code user friendly but also flexible.
Song made by @gpcbass and used on this channel a couple of times. It's called Polar Mist.
Song made by @gpcbass, used previously on this channel.
Visuals in Python & FFmpeg.
1. One ball bouncing inside the egg contour.
2. 10 000 normally distributed balls moving in the same.
3. Same as 2, but larger spread (standard deviation) in initial position and velocity.
Music by @gpcbass . Song called BAYA_street and made today specifically for this visuals.
Visuals in Python & FFmpeg.
1. Ball fired off in a specific direction for both systems.
2. Ball fired off in another specific direction for both systems.
3. Varying starting directions (white = initial direction) spanning between vertical and horizontal direction, where the starting point is fixed.
4. 500 balls equidistantly arranged in the horizontal extension fired off upwards.
Heavily inspired by a mail conversation I had with Max Weinreich who is presently investigating the elliptical curve. Please take a look at arxiv.org/abs/2305.14287 for further mathematical insight.
Music by @gpcbass; song called aLoop and used previously here.
Visuals in Python & FFmpeg.
Music by @gpcbass. Third video in row where the song Polar_Mist is used. I like it very much - that's why.
Visuals in Python & FFmpeg.
In the 1000-ball part balls are initially mutually separated by less than a millionth of the plot width.
Thanks to those suggesting this system! If you announce yourself in the comments, I'll give you credit of course.
Music by @gpcbass. The cool song was also used in our last video, well worth a second listening. It's called Polar_Mist.
Visuals in Python & FFmpeg.
Dope music by @gpcbass. Song is called Polar_mist and made today specifically for this video.
Visuals in Python & FFmpeg.
A few single balls in the circle somehow decided to travel to the future and move backwards in time.
Music by @gpcbass. Song called "Footprints", originally written by Wayne Shorter 1966.
Visuals in Python & FFmpeg.
1. 10000 normally distributed balls dropped symmetrically on f(x) = 0.8|x|
2. Corresponding quantum Gaussian wave packet doing the same.
3. Same as above, but with quantum part as inset for comparison.
Music by @gpcbass; song called GravityY, used previously on this channel.
Visuals in Python & FFmpeg.
1. 5000 normally distributed balls dropped symmetrically on f(x) = |x|
2. Corresponding quantum Gaussian wave packet doing the same.
3. Same as above, but with quantum part as inset for comparison.
Music by @gpcbass - a remake of Bach's Jesus Bleibet meine Freude, used previously on this channel.
Visuals in Python & FFmpeg.
Here, 100 balls, mutually separated by 1e-5 plot width are falling under gravity to hit respective curve.
Music by @gpcbass. Song made yesterday, and called Hip Hip.
Visuals in Python & FFmpeg.
2. 3000 normally distributed balls, aimed to "mimic" the Gaussian wave packet, dropped on a similar parabola.
Music: @gpcbass - Spectrum. Used several times here before.
Visuals in Python & FFmpeg.
The function is indeed minus cos(x) thus having a minimum around origin, but this does of course not impact the conclusion, i.e., that this is a chaotic system. Based on the (visual) conclusion that the x^4 polynomial is chaotic (see youtube.com/watch?v=QyJYkqEsuRE), it's unsurprising that cos(x) is so too, since cos(x) = 1- x^2/2 + x^4/4! - x^6/6! + ...
Balls are initially mutually separated by one millionth of the plot width, and do not interact with each other in any way.
Song: Stella by Starlight, originally made by Victor Young - here reproduced by @gpcbass (and used in several others of our videos).
Visuals in Python & FFmpeg.
The utterly beautiful song is made by @gpcbass, called Vanessa, and previously used a couple of times on this channel. Full version here: youtube.com/watch?v=yE8G0kmfzjc
Visuals in Python and FFmpeg.
For the chaotic system, i.e., the circle, the distance between the balls exhibits a quite clear exponential increase over time, while for the non-chaotic system, the parabola, the distance increases on average linearly.
Song made by @gpcbass, called Bounce it.
Visuals in Python and FFmpeg.
Music by @gpcbass. Song made today specifically for this video and called aLoop.
Visuals in Python & FFmpeg.
Some comments in previous similar videos suggested trying dropping balls on the x^4 function. In contrast to the parabola, x^2, this appears being another chaotic system. 1000 balls, initially mutually spaced apart by approx a millionth of the width of the video, fall under gravity.
Reused music from other videos on this channel, made by @gpcbass. Song is called SEQ2.
Visuals in Python and FFmpeg.
Inspiration from a number of previous comments under the video https://m.youtube.com/watch?v=YoGmq0IdSxk
Beautiful song "For You" by @gpcbass. Used many times before on this channel.
Visuals in Python and FFmpeg.
I tried to "trick" the chaotic system by starting with a couple of hundreds of tightly spaced balls close to the circle boundary, yet they spread out over the whole half disc domain after a short amount of time.
Music by @gpcbass. Song used previously here, and called Top Quark Blues.
Visuals in Python FFmpeg.
As easily seen and previously well known, the balls in the circle exhibit chaotic behaviour after some time, thus demonstrating the butterfly effect. Perhaps surprisingly, the same appears not true for a parabola.
Music by @gpcbass. Song made today specifically for this video and named bounce_it.
Visuals in Python & FFmpeg
Music: @gpcbass - SEQ_1_FUSION
Visuals: Python & FFmeg
Music: Prime Time by @gpcbass (same song as previous video).
Visuals made with Python and FFmpeg.
Music by @gpcbass; song is made today and named Prime Time.
Visuals made in Python and FFmpeg.
Music: @gpcbass - Take3
Visuals: Python & FFmpeg
It is interesting but perhaps not surprising that the nodal lines in some of the states exhibit both hyperbolic and elliptic geometries, also seen in a classical ellipse billiard for a ray trace starting "outside" a focal point (elliptic) and "inside" a focal point (hyperbola).
Music by @gpcbass; another reuse from previous videos here. It's called GravityY.
Visuals done in Python and FFmpeg.
Music: A reproduction of Fjäriln vingad made by @gpcbass. Used in other videos on this channel.
Python & FFmpeg.
Music by @gpcbass. Song is called Top quark blues and already used in another video on this channel.
More specifically, 20 000 double pendulums are released under gravity, initially mutually separated by 1e-6 radians, resulting in chaos and the butterfly effect. Unfortunately, video still suffers from poor bit rate, especially in the wildly chaotic part.
Music by @gpcbass. The song is called Take3, made yesterday for this video.
Visuals in Python and FFmpeg.
Done with Python and FFmpeg.
Song: "Vanessa", made by @gpcbass. Full version: youtube.com/watch?v=yE8G0kmfzjc
Visuals done with Python and FFmpeg.
Music by @gpcbass; a song used many times before on this channel. A reproduction of the absolutely brilliant composition "Jesus bleibet meine Freude", originally made by J S Bach almost 300 years ago. See youtube.com/watch?v=MVsiOKTaCdw and youtube.com/watch?v=WC08VRTqKj0.
svg file downloaded from svgrepo.com
The different runs:
1. Circularly constrained wave packet ("hockey puck") aggressively log plotted, i.e., dark but non-zero probability means really low probability.
2. Gaussian wave packet plotted normally, but colour clipped to emphasise low probability regions.
3. Similar as 2.
I'm quite happy with the photo, and less happy with how the black hole distorts it. Also, the animation magnifies my mediocre post processing skills. 120x30 s, ISO 640, no flattener, unguided, B4 skies, Siril & Gimp. Gear: Nikon D850, Sky-watcher {NEQ6 PRO, Evostar 100ED DS-PRO}.
Animation done with Python and FFmpeg.
Music made by @gpcbass, called SEQ2 (also used previously).


