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Much better visually. We now visualize the 3D version of our stunning Blaschke-Quotient Flow from our previous post.🤗🤩 What follows is a mesmerizing break of dawn in the some realm of complex space with zeros and poles still spinning under SU(1,1) Möbius symmetries on the Poincaré disk…but phase is...

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Mathelirium

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15,826 görüntüleme • 8 ay önce •via X (Twitter)

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A Blaschke-Quotient Flow on the Poincaré Disk Inside the unit disk, zeros and poles perform a Möbius ballet, twisting under SU(1,1) symmetries. Each point follows the gradient of an inner function, its path tracing folds of velvety hyperbolic fabric. Phase interference becomes light bending like thought itself. 🤯🤯🤩🤩🤗🫠
1:00

A Blaschke-Quotient Flow on the Poincaré Disk Inside the unit disk, zeros and poles perform a Möbius ballet, twisting under SU(1,1) symmetries. Each point follows the gradient of an inner function, its path tracing folds of velvety hyperbolic fabric. Phase interference becomes light bending like thought itself. 🤯🤯🤩🤩🤗🫠

Mathelirium

26,382 görüntüleme • 8 ay önce

Hyperbolic waves collide on the Poincaré disk. Bright blooms are constructive peaks, dark bands are cancellations. White tracers ride the phase-gradient, threading filaments. SU(1,1)...the set of Möbius moves that preserve the disk’s geometry...steers the beacons. Multiple tempos modulate the spatial frequency.
2:09

Hyperbolic waves collide on the Poincaré disk. Bright blooms are constructive peaks, dark bands are cancellations. White tracers ride the phase-gradient, threading filaments. SU(1,1)...the set of Möbius moves that preserve the disk’s geometry...steers the beacons. Multiple tempos modulate the spatial frequency.

Mathelirium

30,034 görüntüleme • 9 ay önce

Hyperbolic waves collide on the Poincaré disk. Bright blooms are constructive peaks, dark bands are cancellations. White tracers ride the phase-gradient, threading filaments. SU(1,1)...the set of Möbius moves that preserve the disk’s geometry...steers the beacons. Multiple tempos modulate the spatial frequency.
0:59

Hyperbolic waves collide on the Poincaré disk. Bright blooms are constructive peaks, dark bands are cancellations. White tracers ride the phase-gradient, threading filaments. SU(1,1)...the set of Möbius moves that preserve the disk’s geometry...steers the beacons. Multiple tempos modulate the spatial frequency.

Mathelirium

14,591 görüntüleme • 5 ay önce

This is a living map of a complex rational field: cool regions are root-dominant (|R| 1), where R is the complex rational function. Phase stripes come from arg S (the logarithmic derivative of our complex field R) and particles surf the Newton flow. 🤩🤗😍
1:32

This is a living map of a complex rational field: cool regions are root-dominant (|R| 1), where R is the complex rational function. Phase stripes come from arg S (the logarithmic derivative of our complex field R) and particles surf the Newton flow. 🤩🤗😍

Mathelirium

29,194 görüntüleme • 9 ay önce

You're watching a Quadratic-Differential Teichmüller flow unfold. We drive the scene with a time-varying quadratic differential built from moving zeros and poles. Its log-magnitude sets the color, and its phase defines the horizontal foliation (the direction is half the phase). Then a Teichmüller stretch biases things along vs. against that foliation...so the surface deforms in a geodesic-like way. 🤩🤗🫠
1:26

You're watching a Quadratic-Differential Teichmüller flow unfold. We drive the scene with a time-varying quadratic differential built from moving zeros and poles. Its log-magnitude sets the color, and its phase defines the horizontal foliation (the direction is half the phase). Then a Teichmüller stretch biases things along vs. against that foliation...so the surface deforms in a geodesic-like way. 🤩🤗🫠

Mathelirium

11,938 görüntüleme • 8 ay önce

A stunning strike 🤯 Our Casillero del Diablo countdown of the best Monday night goals is now playing on YouTube 🎬👇
0:24

A stunning strike 🤯 Our Casillero del Diablo countdown of the best Monday night goals is now playing on YouTube 🎬👇

Manchester United

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🚨 What the hell is going on with #XRP?! 🤯🤯 Whale 🐳 just dropped $30 MILLION worth of $XRP in under 60 seconds 🤯 Massive shockwaves hitting the market right now! #Ripple #Crypto #XRPArmy
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🚨 What the hell is going on with #XRP?! 🤯🤯 Whale 🐳 just dropped $30 MILLION worth of $XRP in under 60 seconds 🤯 Massive shockwaves hitting the market right now! #Ripple #Crypto #XRPArmy

Xaif Crypto

112,773 görüntüleme • 1 yıl önce

We now visualize the complex phase of our earlier self-gravitating quantum fluid twisting into smooth helicoids. Think of phase as the wave's "angle" at each point...mapping it to color lets you see how wavefronts curl and shear. Brightness tracks density. The faint moving bands are phase ribbons...contours of equal phase sliding as the field evolves. The tiny white dots are vortices: spots where density dips and the phase wraps by one full turn (2pi). Same Schrödinger-Poisson physics, revealed in phase...live!🫠❤️🫠
0:42

We now visualize the complex phase of our earlier self-gravitating quantum fluid twisting into smooth helicoids. Think of phase as the wave's "angle" at each point...mapping it to color lets you see how wavefronts curl and shear. Brightness tracks density. The faint moving bands are phase ribbons...contours of equal phase sliding as the field evolves. The tiny white dots are vortices: spots where density dips and the phase wraps by one full turn (2pi). Same Schrödinger-Poisson physics, revealed in phase...live!🫠❤️🫠

Mathelirium

14,200 görüntüleme • 9 ay önce

Speech Carries Its Own Hidden Geometry in Phase Space Speech is usually shown as a waveform of amplitude changing in time. Phase-space reconstruction gives a different view by pairing the signal with a delayed version of itself, so the voice is seen as a path rather than just a trace. On the left is the raw sound signal. On the right is the geometric structure formed by rhythm, syllables, and emphasis as the voice unfolds. * Real human speech data from the public GitHub repository voxserv/audio_quality_testing_samples, using the 16 kHz file test01_20s.wav.
0:30

Speech Carries Its Own Hidden Geometry in Phase Space Speech is usually shown as a waveform of amplitude changing in time. Phase-space reconstruction gives a different view by pairing the signal with a delayed version of itself, so the voice is seen as a path rather than just a trace. On the left is the raw sound signal. On the right is the geometric structure formed by rhythm, syllables, and emphasis as the voice unfolds. * Real human speech data from the public GitHub repository voxserv/audio_quality_testing_samples, using the 16 kHz file test01_20s.wav.

Mathelirium

18,725 görüntüleme • 3 ay önce

The Torus Becomes the Canvas A Jacobi Theta Function lives naturally on a complex torus. Instead of drawing it on a flat plane, we wrapped the mathematics onto the torus. The surface is driven by θ₁(z|τ), with its moving zeros, phase winding, and logarithmic derivative shaping the colour, seams, and raised divisor points across the geometry. What you are see is a periodic quantum-like field painted onto the space where it actually belongs. #JacobiTheta #ComplexTorus #MathematicalArt #ComplexAnalysis #RiemannSurfaces #MathAnimation
0:33

The Torus Becomes the Canvas A Jacobi Theta Function lives naturally on a complex torus. Instead of drawing it on a flat plane, we wrapped the mathematics onto the torus. The surface is driven by θ₁(z|τ), with its moving zeros, phase winding, and logarithmic derivative shaping the colour, seams, and raised divisor points across the geometry. What you are see is a periodic quantum-like field painted onto the space where it actually belongs. #JacobiTheta #ComplexTorus #MathematicalArt #ComplexAnalysis #RiemannSurfaces #MathAnimation

Mathelirium

22,197 görüntüleme • 28 gün önce

Phase Space Is the Real Stage of Dynamics. So, Stop Watching the Object and Watch the State. Ordinary Space tells you where something is. Phase Space tells you what state it is in. Position alone is not enough because you also need the variable that tells you where the system is trying to go. In the animation, the left panel shows the particle moving in Ordinary Space, while the right panel shows the same system as a moving point in Phase Space. For one degree of freedom, the state is (x, p) and as time evolves, that state traces a trajectory t ↦ (x(t), p(t)) Instead of thinking of a differential equation as just a formula, Phase Space lets you see it as a flow on the space of states. For this lecture we use ẋ = p ṗ = x − x³ with Hamiltonian H(x,p) = 0.5 p² + 0.25 x⁴ − 0.5 x² #PhaseSpace #DynamicalSystems #NonlinearDynamics #HamiltonianMechanics #Mathematics
0:30

Phase Space Is the Real Stage of Dynamics. So, Stop Watching the Object and Watch the State. Ordinary Space tells you where something is. Phase Space tells you what state it is in. Position alone is not enough because you also need the variable that tells you where the system is trying to go. In the animation, the left panel shows the particle moving in Ordinary Space, while the right panel shows the same system as a moving point in Phase Space. For one degree of freedom, the state is (x, p) and as time evolves, that state traces a trajectory t ↦ (x(t), p(t)) Instead of thinking of a differential equation as just a formula, Phase Space lets you see it as a flow on the space of states. For this lecture we use ẋ = p ṗ = x − x³ with Hamiltonian H(x,p) = 0.5 p² + 0.25 x⁴ − 0.5 x² #PhaseSpace #DynamicalSystems #NonlinearDynamics #HamiltonianMechanics #Mathematics

Mathelirium

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We were in the middle of recording our podcast when the McLaren investigation dropped 🤯🤯🤯
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We were in the middle of recording our podcast when the McLaren investigation dropped 🤯🤯🤯

P1 with Matt & Tommy

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This is how some of our wife's are brainwashed before getting into marriage. What’s happening to the church these days? 🤯🤯🤯🤯🤯🤯🤯🤯🤯
1:07

This is how some of our wife's are brainwashed before getting into marriage. What’s happening to the church these days? 🤯🤯🤯🤯🤯🤯🤯🤯🤯

Mr.Blay

100,828 görüntüleme • 10 ay önce

WHAT HAVE I JUST SEEN. OMFG. ANATOLIY TRUBIN!!! Benfica qualify with the last kick of the league phase! And beat Real Madrid 4-2 in the process 🤯🤯🤯🤯Football on TNT Sports
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WHAT HAVE I JUST SEEN. OMFG. ANATOLIY TRUBIN!!! Benfica qualify with the last kick of the league phase! And beat Real Madrid 4-2 in the process 🤯🤯🤯🤯Football on TNT Sports

Archie Rhind-Tutt

160,968 görüntüleme • 5 ay önce

James Dolan🤯🤯🤯 "Unbelievable goal" from Kildare GAA's James Dolan, we can't tell what was better, the catch or the rocket past Eoin Murphy🤩 Tune in to the Dioralyte Walsh Shield FINAL NOW on #ClubberTV📺
0:28

James Dolan🤯🤯🤯 "Unbelievable goal" from Kildare GAA's James Dolan, we can't tell what was better, the catch or the rocket past Eoin Murphy🤩 Tune in to the Dioralyte Walsh Shield FINAL NOW on #ClubberTV📺

Clubber

25,782 görüntüleme • 5 ay önce

🚨 NOW: President Trump takes huge VICTORY LAP on the success of Space Force — which some Democrats MOCKED Space Force is now vastly improving the accuracy of our weapons on the ground. And we're leading China and Russia, easily 🔥 "I'm very proud of the Space Force because that was a branch that a new one that came up, and we were losing to Russia and to China in space." "Space Force is now leading the other countries, China, Russia, and there is no fourth, really, and leading them by, we saw numbers the other day, leading, we're leading in space by so much it's, we're never going to be caught. So I'm very proud of Space Force!" "I think it's going to be one of our most important as time goes by. A lot of the things that you see, a lot of the accuracy of the weapons is caused because of what we created with Space Force, so we're very proud of that."
1:05

🚨 NOW: President Trump takes huge VICTORY LAP on the success of Space Force — which some Democrats MOCKED Space Force is now vastly improving the accuracy of our weapons on the ground. And we're leading China and Russia, easily 🔥 "I'm very proud of the Space Force because that was a branch that a new one that came up, and we were losing to Russia and to China in space." "Space Force is now leading the other countries, China, Russia, and there is no fourth, really, and leading them by, we saw numbers the other day, leading, we're leading in space by so much it's, we're never going to be caught. So I'm very proud of Space Force!" "I think it's going to be one of our most important as time goes by. A lot of the things that you see, a lot of the accuracy of the weapons is caused because of what we created with Space Force, so we're very proud of that."

Eric Daugherty

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This spinning elbow is the KO of the YEAR! 🤯
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This spinning elbow is the KO of the YEAR! 🤯

Kirgo.com

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A good description of our True Realm. We live on a vast, stationary flat plane, not a spinning ball in space. At the center is the North Pole, with continents spreading outward. The outer edge is surrounded by an impassable Antarctic ice wall that contains the oceans. Above us is the firmament....a rotating dome with the Sun, Moon, and stars circling overhead, creating day and night. There is no outer space or globe Earth as we are now seeing through the BS coming from Artemis and NASA . We inhabit a beautiful, enclosed, purposeful creation on solid, level ground under a close sky. This is our real world.
1:52

A good description of our True Realm. We live on a vast, stationary flat plane, not a spinning ball in space. At the center is the North Pole, with continents spreading outward. The outer edge is surrounded by an impassable Antarctic ice wall that contains the oceans. Above us is the firmament....a rotating dome with the Sun, Moon, and stars circling overhead, creating day and night. There is no outer space or globe Earth as we are now seeing through the BS coming from Artemis and NASA . We inhabit a beautiful, enclosed, purposeful creation on solid, level ground under a close sky. This is our real world.

DeepWebSlinger

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IMOV IS COMING TO RULE THE SPACE 🚀 IMOV IS THE MOST WATCHED PROJECT IN BSC RIGHT NOW 🔥🤯 JOIN US NOW THE REAL STORM IS ABOUT TO START 🤯 CHECK NOW OUR BIG PRODUCTS: #IMOV #IMT #BNB #IMOVCHAIN #IMOVPRODUCTS
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IMOV IS COMING TO RULE THE SPACE 🚀 IMOV IS THE MOST WATCHED PROJECT IN BSC RIGHT NOW 🔥🤯 JOIN US NOW THE REAL STORM IS ABOUT TO START 🤯 CHECK NOW OUR BIG PRODUCTS: #IMOV #IMT #BNB #IMOVCHAIN #IMOVPRODUCTS

Imov

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