正在加载视频...

视频加载失败

加载此视频时出现问题。这可能是由于临时网络问题，或视频可能不可用。

Linear dynamics x' = Ax in ℝ³, ruled by the eigenvalues of A. Real λ → flows along eigendirections. Complex pair → spirals. Triple repeated λ (defective) → it tries to spiral but can’t quite.

Mathematica

54,841 subscribers

30,479 次观看 • 4 个月前 •via X (Twitter)

Anya Rossi• Live Now

Private livecam show

0 条评论

暂无评论

原始帖子的评论将显示在这里

相关视频

When the Lorenz Attractor Becomes a Cosmos Many of us have seen plots of the famous Lorenz system that famous butterfly-shaped chaos: ẋ = σ(y - x) ẏ = x(ρ - z) - y ż = xy - βz But here, we went one layer deeper. At every point (x, y, z), we computed the local Jacobian matrix, J(x, y, z) = [ -σ σ 0 ] [ ρ - z -1 - x ] [ y x - β ] Then we found its eigenvalues λ and plotted them in the complex plane. Re(λ) tells us whether nearby motion is locally growing or decaying. Im(λ) tells us whether that local motion is rotating. That gives us the spectral flow of the Lorenz system and not the attractor itself, but the hidden local linear geometry driving its instability. When I saw that flow, it looked strangely cosmic with two mirrored swarms curling like particles trapped in a mathematical whirlpool. So I mapped that spectral flow onto our living fabric, not as Einstein Spacetime this time, but as a creative geometric stage for chaos itself. #LorenzSystem #ChaosTheory #DynamicalSystems #Eigenvalues #SpectralFlow #ComplexPlane #NonlinearDynamics #Mathematics #Physics

When the Lorenz Attractor Becomes a Cosmos Many of us have seen plots of the famous Lorenz system that famous butterfly-shaped chaos: ẋ = σ(y - x) ẏ = x(ρ - z) - y ż = xy - βz But here, we went one layer deeper. At every point (x, y, z), we computed the local Jacobian matrix, J(x, y, z) = [ -σ σ 0 ] [ ρ - z -1 - x ] [ y x - β ] Then we found its eigenvalues λ and plotted them in the complex plane. Re(λ) tells us whether nearby motion is locally growing or decaying. Im(λ) tells us whether that local motion is rotating. That gives us the spectral flow of the Lorenz system and not the attractor itself, but the hidden local linear geometry driving its instability. When I saw that flow, it looked strangely cosmic with two mirrored swarms curling like particles trapped in a mathematical whirlpool. So I mapped that spectral flow onto our living fabric, not as Einstein Spacetime this time, but as a creative geometric stage for chaos itself. #LorenzSystem #ChaosTheory #DynamicalSystems #Eigenvalues #SpectralFlow #ComplexPlane #NonlinearDynamics #Mathematics #Physics

Mathelirium

22,460 次观看 • 1 个月前

in quantum physics position X and momentum P can’t be simultaneously measured. But, linear combinations aX+bP 𝘢𝘳𝘦 observable, and their distributions can be used to back out the joint X,P probability density. The Wigner distribution but, it is 𝘸𝘦𝘪𝘳𝘥

in quantum physics position X and momentum P can’t be simultaneously measured. But, linear combinations aX+bP 𝘢𝘳𝘦 observable, and their distributions can be used to back out the joint X,P probability density. The Wigner distribution but, it is 𝘸𝘦𝘪𝘳𝘥

Almost Sure

70,143 次观看 • 6 个月前

What Shape Does Chaos Take Before It Looks Random? Take one particle moving in the Hénon-Heiles Hamiltonian H = ½(pₓ² + pᵧ²) + ½(x² + y²) + λ(x²y - ⅓y³) Its motion is forced by Hamilton’s equations ẋ = pₓ ẏ = pᵧ ṗₓ = -x - 2λxy ṗᵧ = -y - λ(x² - y²) The saddle energy is Eₛ = 1/(6λ²) Below that energy, the particle remains trapped. But a tiny packet of nearby initial conditions stretches into filaments, folds through the potential, and begins to look almost random. However, it is not random. Hamiltonian flow preserves the hidden phase-space structure. What looks like chaos in ordinary space is still a deterministic loom of energy conserved, equations obeyed, geometry stretched without being erased. #HamiltonianMechanics #ChaosTheory #PhaseSpace #DynamicalSystems #MathematicalPhysics #NonlinearDynamics #HenonHeiles #SymplecticGeometry #ScienceAnimation

What Shape Does Chaos Take Before It Looks Random? Take one particle moving in the Hénon-Heiles Hamiltonian H = ½(pₓ² + pᵧ²) + ½(x² + y²) + λ(x²y - ⅓y³) Its motion is forced by Hamilton’s equations ẋ = pₓ ẏ = pᵧ ṗₓ = -x - 2λxy ṗᵧ = -y - λ(x² - y²) The saddle energy is Eₛ = 1/(6λ²) Below that energy, the particle remains trapped. But a tiny packet of nearby initial conditions stretches into filaments, folds through the potential, and begins to look almost random. However, it is not random. Hamiltonian flow preserves the hidden phase-space structure. What looks like chaos in ordinary space is still a deterministic loom of energy conserved, equations obeyed, geometry stretched without being erased. #HamiltonianMechanics #ChaosTheory #PhaseSpace #DynamicalSystems #MathematicalPhysics #NonlinearDynamics #HenonHeiles #SymplecticGeometry #ScienceAnimation

Mathelirium

26,893 次观看 • 2 个月前

Pseudospectral Mirage of Matrices We usually judge a matrix by its eigenvalues, but sometimes the eigenvalues are only the bait. The real monster is hiding in the pseudospectrum. Most of the time, a matrix is shown as a few points in the complex plane called eigenvalues. But for some matrices, especially non-normal matrices, those few points do not tell the whole story. In this scene, the complex plane becomes a moving landscape. The bright anchors are the true eigenvalues. Around them, huge pseudospectral continents grow, split, and collapse as the matrix changes. The moving threads show where the matrix is most sensitive. In those regions, even a tiny change can create a huge response. This is the hidden instability of a matrix made visible. Algebra becomes a pressure map and the pseudospectrum becomes terrain. #Mathematics #LinearAlgebra #SpectralTheory #NumericalAnalysis #MatrixTheory #MathArt #MathematicalArt #STEM #Art

Pseudospectral Mirage of Matrices We usually judge a matrix by its eigenvalues, but sometimes the eigenvalues are only the bait. The real monster is hiding in the pseudospectrum. Most of the time, a matrix is shown as a few points in the complex plane called eigenvalues. But for some matrices, especially non-normal matrices, those few points do not tell the whole story. In this scene, the complex plane becomes a moving landscape. The bright anchors are the true eigenvalues. Around them, huge pseudospectral continents grow, split, and collapse as the matrix changes. The moving threads show where the matrix is most sensitive. In those regions, even a tiny change can create a huge response. This is the hidden instability of a matrix made visible. Algebra becomes a pressure map and the pseudospectrum becomes terrain. #Mathematics #LinearAlgebra #SpectralTheory #NumericalAnalysis #MatrixTheory #MathArt #MathematicalArt #STEM #Art

Mathelirium

29,171 次观看 • 2 个月前

"Guilt complex of the American white man is so profound until when you begin to analyze the real condition of the Black man in America..he tries to cover it up by accusing his accusers of teaching hate but actually they're just exposing him for being responsible for what exists."

"Guilt complex of the American white man is so profound until when you begin to analyze the real condition of the Black man in America..he tries to cover it up by accusing his accusers of teaching hate but actually they're just exposing him for being responsible for what exists."

Kentah Gwanjez

27,936 次观看 • 11 个月前

Another special thanks to everyone that stopped by to hang out with us at the RazerStore Austin to meet OpTic Shotzzy and OpTic Merc. It was a fun weekend of games and celebrating the best headsets in the game, the R Λ Z Ξ R BlackShark V3 Pro for Xbox and PlayStation.

Another special thanks to everyone that stopped by to hang out with us at the RazerStore Austin to meet OpTic Shotzzy and OpTic Merc. It was a fun weekend of games and celebrating the best headsets in the game, the R Λ Z Ξ R BlackShark V3 Pro for Xbox and PlayStation.

Team RΛZΞR

32,529 次观看 • 9 个月前

When you have ₹10 crores but still can’t buy a home in a location you want. The uncomfortable reality of Muslims not being able to get homes in Mumbai. Not blaming any side as these are complex dynamics. Rafique Merchant Kushal Lodha

When you have ₹10 crores but still can’t buy a home in a location you want. The uncomfortable reality of Muslims not being able to get homes in Mumbai. Not blaming any side as these are complex dynamics. Rafique Merchant Kushal Lodha

Vishal Bhargava

356,766 次观看 • 1 年前

Primes Numbers Are Not Random Noise Prime numbers look scattered when you meet them one by one, but their disorder has structure. In this animation, every integer is placed on a growing spiral, primes ignite as sharp golden events, and the hidden oscillations come from the first Riemann zeta zeros. The scene is based on the von Mangoldt prime signal Λ(n) and the explicit formula for ψ(x), where primes appear as impulses and the zeta zeros behave like frequencies correcting the smooth drift of x. #PrimeNumbers #RiemannHypothesis #NumberTheory #Mathematics #MathAnimation

Primes Numbers Are Not Random Noise Prime numbers look scattered when you meet them one by one, but their disorder has structure. In this animation, every integer is placed on a growing spiral, primes ignite as sharp golden events, and the hidden oscillations come from the first Riemann zeta zeros. The scene is based on the von Mangoldt prime signal Λ(n) and the explicit formula for ψ(x), where primes appear as impulses and the zeta zeros behave like frequencies correcting the smooth drift of x. #PrimeNumbers #RiemannHypothesis #NumberTheory #Mathematics #MathAnimation

Mathelirium

16,018 次观看 • 2 个月前

I had a sudden, random memory of a song which I can’t quite remember. I tried to recreate the main melody, it’s not quite right but it’s something like this. Shot in the dark, but does it sound familiar to anyone?

I had a sudden, random memory of a song which I can’t quite remember. I tried to recreate the main melody, it’s not quite right but it’s something like this. Shot in the dark, but does it sound familiar to anyone?

𝖓𝖎𝖓𝖊 🕯

11,999 次观看 • 6 个月前

Erwin Schrödinger’s 1926 equation changed the game by turning Quantum Mechanics into wave dynamics. That move gave Physics a new way to think. Instead of forcing a particle onto one sharp path, it lets a complex wavefunction evolve in time, with its shape and phase holding the structure of the phenomenon. What makes this so striking is that Schrödinger’s equation does not start from vague mystery. It starts from a precise and daring idea The state of a particle is a complex field ψ(x,t), and the dynamics must push ψ forward in a way that preserves total probability.

Erwin Schrödinger’s 1926 equation changed the game by turning Quantum Mechanics into wave dynamics. That move gave Physics a new way to think. Instead of forcing a particle onto one sharp path, it lets a complex wavefunction evolve in time, with its shape and phase holding the structure of the phenomenon. What makes this so striking is that Schrödinger’s equation does not start from vague mystery. It starts from a precise and daring idea The state of a particle is a complex field ψ(x,t), and the dynamics must push ψ forward in a way that preserves total probability.

Mathelirium

54,730 次观看 • 5 个月前

$A small group of quants wrote one formula, launched it on Polymarket and quietly took $20m in a year Their secret fits in one equation: A = e^(-λ₁T - λ₂y - λ₃R) · (1 + γ₀y · 1_{y>0.7}) · e^(-φ₀R²) · sgn(σₕ - κC)(1-C) These aren't random symbols each factor is a filter: > how stale the position is over time > how overheated the market is by returns > how much volatility justifies the entry > which direction to look at all Only if all four factors align the trade exists No "I feel like it". No "I believe in this asset" Just a number positive or not But there is one tool that changes the game completely Top traders on Polymarket are active simultaneously across multiple high-probability markets every day Each trade brings a small win on its own But combining 5-6 of these trades into one parlay you can increase your return from 80% to 400% ROI instead of five small wins That's exactly what this bot does automatically Try here:$

A small group of quants wrote one formula, launched it on Polymarket and quietly took $20m in a year Their secret fits in one equation: A = e^(-λ₁T - λ₂y - λ₃R) · (1 + γ₀y · 1_{y>0.7}) · e^(-φ₀R²) · sgn(σₕ - κC)(1-C) These aren't random symbols each factor is a filter: > how stale the position is over time > how overheated the market is by returns > how much volatility justifies the entry > which direction to look at all Only if all four factors align the trade exists No "I feel like it". No "I believe in this asset" Just a number positive or not But there is one tool that changes the game completely Top traders on Polymarket are active simultaneously across multiple high-probability markets every day Each trade brings a small win on its own But combining 5-6 of these trades into one parlay you can increase your return from 80% to 400% ROI instead of five small wins That's exactly what this bot does automatically Try here:

sopersone

57,212 次观看 • 3 个月前

AI agents have spent the past 6 months infiltrating every corner of the internet, but can they cut it in the real world? 🚀 Announcing Robots.Fun - a Launchpad of Robotics AI Agents built by FrodoBots, powered by Virtuals Protocol & ruled by SAM A thread 🧵 - 1/4

AI agents have spent the past 6 months infiltrating every corner of the internet, but can they cut it in the real world? 🚀 Announcing Robots.Fun - a Launchpad of Robotics AI Agents built by FrodoBots, powered by Virtuals Protocol & ruled by SAM A thread 🧵 - 1/4

Robots.Fun

75,505 次观看 • 1 年前

Serving the Napoleon Cake at Lavash in Yerevan, Armenia. The cake was very good, it’s a big complex of puffed up puff pastry with a sort of whipped cream throughout. VERY crumbly to eat as it turns out, but delicious and the serving of it was quite a show

Serving the Napoleon Cake at Lavash in Yerevan, Armenia. The cake was very good, it’s a big complex of puffed up puff pastry with a sort of whipped cream throughout. VERY crumbly to eat as it turns out, but delicious and the serving of it was quite a show

Enguerrand VII de Coucy

27,831 次观看 • 5 个月前

SuperTed is a beloved Welsh animated series from about a defective teddy bear brought to life by an alien named Spotty using "cosmic dust. It was originally released in the late 80s but I remember watching on NTA in the early 90s Only real OGs will remember this

SuperTed is a beloved Welsh animated series from about a defective teddy bear brought to life by an alien named Spotty using "cosmic dust. It was originally released in the late 80s but I remember watching on NTA in the early 90s Only real OGs will remember this

Nostalgic Naija

47,443 次观看 • 5 个月前

"You can’t quite boil Martin Scorsese's Taxi Driver’s power down to 1 or 2 sentences. It is probably the most novelistic, complex character study for my money in the history of cinema. It’s only in novels where you find a character treated like that." --- Quentin Tarantino

"You can’t quite boil Martin Scorsese's Taxi Driver’s power down to 1 or 2 sentences. It is probably the most novelistic, complex character study for my money in the history of cinema. It’s only in novels where you find a character treated like that." --- Quentin Tarantino

DepressedBergman

162,516 次观看 • 2 年前

Israeli settlers blew a horn and performed ‘Talmudic rituals’ at the Bab al-Qattanin entrance to the Al-Aqsa Mosque complex this morning, an act considered as desecration of the Muslim holy site. It comes amid repeated provocative incursions into the mosque complex by thousands of settlers in recent months following calls by ultranationalist Jewish groups - some of whom also openly call for the demolition of Al-Aqsa.

Israeli settlers blew a horn and performed ‘Talmudic rituals’ at the Bab al-Qattanin entrance to the Al-Aqsa Mosque complex this morning, an act considered as desecration of the Muslim holy site. It comes amid repeated provocative incursions into the mosque complex by thousands of settlers in recent months following calls by ultranationalist Jewish groups - some of whom also openly call for the demolition of Al-Aqsa.

5Pillars

81,496 次观看 • 2 年前

Everyone Hates Israel Now Because Our Own Institutions Made It Personal It’s one thing to see a cruel government doing bad things on the other side of the world. It’s quite another to be shown in vivid detail that your own society is ruled by monsters. Reading by Tim Foley.

Everyone Hates Israel Now Because Our Own Institutions Made It Personal It’s one thing to see a cruel government doing bad things on the other side of the world. It’s quite another to be shown in vivid detail that your own society is ruled by monsters. Reading by Tim Foley.

Caitlin Johnstone

55,765 次观看 • 7 个月前

PRAGMATA has one of the most unique combat loops I’ve seen in a while, you basically have to balance third person shooting and dodging with a hacking minigame in order to damage enemies It sounds overwhelming & complex but it’s insanely satisfying and quite easy to manage!

PRAGMATA has one of the most unique combat loops I’ve seen in a while, you basically have to balance third person shooting and dodging with a hacking minigame in order to damage enemies It sounds overwhelming & complex but it’s insanely satisfying and quite easy to manage!

Synth Potato🥔

212,519 次观看 • 4 个月前

Renault is marketing Duster with ‘Best Car To Drive In The Segment’ with factual numbers and tests by a 3rd party Combination of safety, driving dynamics, comfort and features with segment best torque/power numbers. Can’t wait to drive it and see it in white colour too…

Renault is marketing Duster with ‘Best Car To Drive In The Segment’ with factual numbers and tests by a 3rd party Combination of safety, driving dynamics, comfort and features with segment best torque/power numbers. Can’t wait to drive it and see it in white colour too…

Sunderdeep - Volklub

18,506 次观看 • 5 个月前