Ten million balls in a superellipse billiard (chaotic) Alexander Gustafsson 2025-09-29 | Ten million balls confined in a superellipse billiard, (x/a)^4 + (y/b)^4 = 1, are released with a couple of different initial configurations in space and velocity. Music by @gpcbass - this cool song is called "Here it is".Visuals in Mathematica.
Vader stringart Alexander Gustafsson 2025-02-25 | Some Starwars stringart is shown. I rendered the frames in 1080p and then upscaled the images to 4k in hope for easier recognizing the faces involved. However, you still might want to squint for easier recognition :). The homemade stringart code can be found at my github, alguaa/animations_ag.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=No0wjSw0T9cVisuals in Python and FFmpeg
Gravitationally interacting balls in an ellipse billiard Alexander Gustafsson 2025-01-21 | Two gravitationally interacting balls move in an ellipse billiard. The balls are point-like and cannot collide even though their depicted size indicate that the could. The softening of the gravitational potential is quite exaggerated to avoid excessive speeds when the balls pass very close to each other.Music by @gpcbass. The song, made yesterday, is called Dance Floor.Visuals in Mathematica.
Gravity inside and outside a spherical shell Alexander Gustafsson 2025-01-18 | This silly and somewhat buggy little video shows some physics that i found very interesting once upon a time when I was a physics student. 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.htmlBeautiful music by @gpcbass and Rogge. It's a Bach reproduction. Full version and more info here: youtube.com/watch?v=1LUzDOIIFO0Visuals in Mathematica
Wave packet propagation in different lattices Alexander Gustafsson 2025-01-03 | Another wave packet propagation animation, where the wave evolves according to the ordinary time-dependent Schrödinger equation by utilizing the Fourier split step method. The real space domain has the dimensions 3840x2160, i.e., 4k, for all four runs, which is quite time consuming to compute. The lattices are modeled using Gaussian shaped bumps. That is, the potential is zero everywhere except at the lattice points (marked as dots as the centers for the Gaussians, for visual purposes) where the potential is positive.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.
Reinforcement learning agents improving maze solving skills Alexander Gustafsson 2024-12-27 | Not my proudest work from a visual point of view - especially not since a GPT helped me a lot with the coding and bug fixing. That is, a machine helped me to learn a machine.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.
One million balls dropped on functions Alexander Gustafsson 2024-10-16 | One million balls are dropped on |x|, x^2, and interior of circle, x^2 + y^2 = 1.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.
Millions of particles forming cardioid caustics in a circle billiard Alexander Gustafsson 2024-10-04 | This is a classical counterpart of the quantum circle billiard uploaded yesterday: youtube.com/watch?v=akh7KbPyOBISimulation 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.
Cardioid caustics in a quantum circle billiard Alexander Gustafsson 2024-10-03 | The split step Fourier method was used, allowing for efficient and seemingly accurate high resolution wave propagation of a Gaussian wave packet according to the Schrödinger equation. 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.
Liquid fractal emergence Alexander Gustafsson 2024-07-25 | The Mandelbrot set is generated with stepwise incremental of iterations and intermediate zooming onto a specific coordinate in the so-called Seahorse valley. 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).
Triple pendulum chaos Alexander Gustafsson 2024-07-09 | Motion of the triple pendulum is shown, displaying a highly chaotic behavior. The latter part shows 5000 triple pendulums initially mutually spaced apart by a millionth of a radian.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.
How cats actually land (slo-mo softbody) Alexander Gustafsson 2024-06-19 | Two-dimensional softbody simulation of a cat landing on a floor. Muscular forces are visualized too, where red is stronger, and violet/white are weaker forces.Music: @gpcbass; song called Minor Step
Triceratops softbody Alexander Gustafsson 2024-06-11 | A two-dimensional softbody having the shape of a triceratops skips resiliently on a floor.A MWE softbody code can be found on my git.Music made yesterday by @gpcbass. Song is called Ancient Jumper.Visuals in Python & FFmpeg.
Phase space moose Alexander Gustafsson 2024-05-12 | Short intro to phase spaces in dynamical billiards followed by 6000 points confined to the interior of a moose-shaped contour moving in a superellipse billiard (x^2 + y^2/b^2 = 1). 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
Moose dropped on a parabola Alexander Gustafsson 2024-03-13 | 3000 randomly distributed point masses initialized to be confined to the interior of a moose-shaped contour are released under gravity to scatter off the function f(x) = x^2. As with the function f(x) = |x|, this is also a non-chaotic system and the points spread out linearly over time and render a rather interesting transformation of the moose points. 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.
Moose dropped on a simple mathematical function (plus annoying bugs) Alexander Gustafsson 2024-03-10 | The moose series never ends, apparently. 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.
Gravitational collapse of a moose Alexander Gustafsson 2024-03-05 | 500 000 gravitationally interacting initially unrelaxed point masses are randomly distributed inside a moose contour and released to demonstrate a devastating gravitational collapse of the moose.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.
Photographing a trillion-star galaxy (quick-and-dirty how-to) Alexander Gustafsson 2024-02-25 | Shown is an image I took earlier this year of one of the most majestic galaxies as seen from us; the M101 (so-called Pinwheel galaxy). It's located about 20 million lightyears from us and houses approx 1 trillion stars. Its face-on characteristic is a truly spectacular sight.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
(Super)ellipse billiard Alexander Gustafsson 2024-02-05 | An ellipse (x^2 + (y/a)^2 = 1) and a superellipse (x^4 + (y/a)^4 = 1) billiard are compared by executing 100 linearly arranged balls in the same direction.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.
Bad stringart Alexander Gustafsson 2023-11-13 | I finally had some success with my little stringart project in python. 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.
Hourglass billiard Alexander Gustafsson 2023-07-07 | Ball/ray moving and elastically bouncing in a domain reminiscent of an hourglass. Pretty useless for being an hourglass though.Song made by @gpcbass, used previously on this channel.Visuals in Python & FFmpeg.
Egg billiard Alexander Gustafsson 2023-06-12 | Balls elastically bouncing in a two dimensional egg-shaped mathematical billiard are shown. The egg contour is defined by x^2 + (1.4^x * 1.6y)^2 = 1 (equation discovered by Don M. Jacobs).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.
Butterfly effect in an elliptic curve but not in an ellipse Alexander Gustafsson 2023-06-04 | Billiard comparison between the bounded region of the function y^2 = x^3 - x (elliptic curve; see wolframalpha.com/input?i=y%5E2+%3D+x%5E3-x) and x^2 + ay^2 = 1 (ellipse). For certain initial conditions, the elliptical curve system exhibits a chaotic behaviour, i.e., "butterfly effect" in contrast to the ellipse. 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.
Squircle billiard Alexander Gustafsson 2023-05-28 | 5000 normally distributed balls having the same initial moving direction are shown for the system |x|^n + |y|^n = 1, for n = 1 (square), n = 2 (circle), and n = 4 (squircle - yes, they have actually named this shape so).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.
Balls dropped on a double well curve (~ x^4 - x^2) Alexander Gustafsson 2023-05-15 | 1, 2, and 1000 balls dropped on the function y = x^4 - 3x^2.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.
Mandelbrot set: simple equation - complex boundary Alexander Gustafsson 2023-05-09 | Some standard basics regarding the famous Mandelbrot set fractal are presented. Needed prior knowledge is familiarity with complex numbers.Dope music by @gpcbass. Song is called Polar_mist and made today specifically for this video.Visuals in Python & FFmpeg.
5000 balls falling in a circle and a parabola, plus a cute bug Alexander Gustafsson 2023-04-28 | 5000 initially randomly homogeneously distributed balls arranged as a circular disc fall on a lower half circle boundary and on a parabola.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.
10000 classical balls and quantum wave packet falling on 0.8|x| Alexander Gustafsson 2023-04-22 | Let's see what the bitrate devil says about this... (3.10 min video = 650 MB)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.
5000 classical balls and quantum wave packet falling on |x| Alexander Gustafsson 2023-04-19 | Yet another ball drop one, sorry... The patterns emerging here are quite odd and visually appealing imo, though.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.
Balls dropped on functions 0.5*|x| and 2*|x| = chaos Alexander Gustafsson 2023-04-18 | Inspired by a comment from @Wade Hodson in the video youtube.com/watch?v=7Ae_-sL2kFw (balls dropped on |x|). As mentioned in that comment a chaotic behaviour can be observed for a*|x|, a being smaller or larger than 1. 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.
Quantum and classical balls dropped on a parabola Alexander Gustafsson 2023-04-15 | 1. Gaussian wave packet dropped under gravity (or electric field) on a parabola y = 2.2x^2. Discrete domain spanned by approx 800x1200 lattice points.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.
Balls falling on cos(x) Alexander Gustafsson 2023-04-13 | Suggested by several viewers in another videos. Thanks for commenting and suggesting stuff.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.
Balls dropped on function |x| Alexander Gustafsson 2023-04-12 | Another drop-balls-on-a-function video; here on f(x) = |x|. 100 balls, initially mutually separated by 1e-4 plot width.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=yE8G0kmfzjcVisuals in Python and FFmpeg.
Butterfly effect in a circle but not in a parabola, with graphs Alexander Gustafsson 2023-04-04 | Similar to the video youtube.com/watch?v=0zmWEzrtvJA, but here with only two balls each, and including graphs over incremental separation between balls over time. For the parabola, the initial separation is 1e-3 length units, while for the circle the initial separation is much smaller, 1e-7 length units. For reference, the radius of the circle is 1 length unit.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.
Balls symmetrically dropped in a parabola Alexander Gustafsson 2023-04-02 | 201 balls dropped in a parabola creating some interesting patterns while time passes.Music by @gpcbass. Song made today specifically for this video and called aLoop.Visuals in Python & FFmpeg.
Balls falling on a quartic function Alexander Gustafsson 2023-04-01 | Let's see how far I can exploit the recommendation algorithm...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.
Balls dropped on a hyperbola Alexander Gustafsson 2023-03-28 | Balls initially mutually separated by approx one millionth of the plot width, dropped on the hyperbola y^2 - x^2 = 1 (positive root). The video is quite slow but eventually exhibits chaotic behaviour of the balls, i.e., the butterfly effect. 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.
Butterfly effect in a circle, again Alexander Gustafsson 2023-03-25 | Trivial iteration from the video youtube.com/watch?v=YoGmq0IdSxk&lc=UgyLu3bDr2kPpbWzDRN4AaABAgI 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.
Butterfly effect in a circle but not in a parabola Alexander Gustafsson 2023-03-22 | 200 balls released in a circle (x^2 + y^2 = 1) and a parabola (y = x^2) respectively. In respective system the balls are initially mutually separated by a small distance. The initial ball distribution is same for both systems.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
Stadium-, circle-, and ellipse probability densities Alexander Gustafsson 2023-03-12 | Some probability densities (|eigenvector|^2) are shown for three quantum systems.Music: @gpcbass - SEQ_1_FUSIONVisuals: Python & FFmeg
Ellipse reminds you of its focal points Alexander Gustafsson 2023-03-04 | A couple of hundreds of balls are arranged along a vertical line at the center of an ellipse boundary whereafter they all move towards a point on the reflective boundary. Music: Prime Time by @gpcbass (same song as previous video).Visuals made with Python and FFmpeg.
Billiard of expressions, fruits, symmetry, etc. Alexander Gustafsson 2023-03-01 | A couple of hundreds of balls starting along a centered line at equal speed, and hitting a single point at the circle boundary, balls over time making some "funny" patterns. Music by @gpcbass; song is made today and named Prime Time.Visuals made in Python and FFmpeg.
Relatively unpopular double pendulum animation Alexander Gustafsson 2023-02-15 | This video - youtube.com/watch?v=ldnEHycw40E - will reach one million views within hours. It was suddenly picked up by the idiosyncratic algorithm in 2021 and gained massive attention during a couple of weeks whereafter its "popularity" stagnated significantly. It will pass the magic milestone though. The present video, although much smoother, will probably never experience anything near that.Music: @gpcbass - Take3Visuals: Python & FFmpeg
Eigenfunctions of an ellipse Alexander Gustafsson 2023-01-30 | Another eigenfunction video, here for the precious ellipse blessing this channel so far with approx 70k thumbs up.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.
Penrose unilluminable room eigenfunctions Alexander Gustafsson 2023-01-27 | Python and FFmpeg.Music: A reproduction of Fjäriln vingad made by @gpcbass. Used in other videos on this channel.
Moose eigenfunctions Alexander Gustafsson 2023-01-24 | Eigenfunctions of a moose-shaped tensioned membrane, or, equivalently, a quantum well having a floor shaped as a moose.Python & FFmpeg.Music by @gpcbass. Song is called Top quark blues and already used in another video on this channel.
Yet another dull double pendulum video Alexander Gustafsson 2023-01-17 | Another one, sorry... On and off I'm randomly searching for small but incremental improvements for setups like these. Shifting color schemes is something "new" here, as well as other small adjustments/improvements.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.
Optical illusion by Fourier epicycles Alexander Gustafsson 2023-01-12 | Optical illusion reproduced and modified from newopticalillusions.com/funny-optical-illusions/crazy-stair/.Done with Python and FFmpeg.Song: "Vanessa", made by @gpcbass. Full version: youtube.com/watch?v=yE8G0kmfzjc
Quantum moose billiard Alexander Gustafsson 2023-01-04 | Actually three different runs. In each a wave function (plotted absolute squared) evolves in a quantum well formed as a moose. The discrete domain is approx. 1400x1400 lattice points.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.comThe 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.
Orion Nebula obscured and warped by a black hole Alexander Gustafsson 2023-01-02 | This video is essentially identical to another video on this channel from an animation point of view. Since this is the first image I've ever taken with my new telescope, and since I neither have intentions to transform this channel to an astrophoto channel, nor create a new channel with this theme, this was how it had to be this time.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).
