When Light Folds Into a Cusp A smooth wavefront can focus into something sharp, bright, and almost impossible-looking... a Caustic. This scene is built from the Pearcey diffraction integral, P(a,b) = ∫ exp(i(t⁴ at² bt)) dt, one of the canonical objects in Catastrophe Optics. The variables a and b unfold a cusp catastrophe. As they change, the wave does not simply brighten smoothly, it folds into sharp luminous curves, then breaks into diffraction fringes around the cusp. The visible intensity is I(a,b) = |P(a,b)|², and the colour carries the complex phase arg P. This is the Mathematics behind the bright cusps you see in focused light, water caustics, optical lenses, and wavefields near singular focusing events. #CatastropheTheory #Optics #WavePhysics #MathematicalPhysics #PhysicsVisualization #Caustics

The Fluid That Organizes Its Own Chaos A 2D fluid can do something strange. Tiny vortices can self-organize into giant rotating clusters. This is Onsager’s vortex gas. Each vortex has a circulation Γᵢ, and its position zᵢ = xᵢ iyᵢ moves because of every other vortex: ẋᵢ = −Σⱼ Γⱼ(yᵢ−yⱼ)/(2πrᵢⱼ²), ẏᵢ = Σⱼ Γⱼ(xᵢ−xⱼ)/(2πrᵢⱼ²), with rᵢⱼ² = (xᵢ−xⱼ)² (yᵢ−yⱼ)². The surprise is that this chaotic-looking Hamiltonian system can build order. Same-sign vortices gather into large coherent continents, while opposite signs carve turbulent borders between them. In this animation, the dots evolve by the point-vortex equations, while the screen renders the signed vorticity field ω(x,y,t) = Σᵢ Γᵢ exp(−|r−rᵢ(t)|²/2σ²). Blue and cyan show one circulation direction. Gold and coral show the other. Order appears out of rotation. #FluidDynamics #Vortices #OnsagerVortices #MathematicalPhysics #PhysicsVisualization #Turbulence

Magnetic Flux Turns a Torus Into a Wavefunction A quantum particle is confined to a torus, with magnetic flux threading through its two closed cycles. The eigenstates are twisted momentum waves, Ψₘₙ(u,v) = exp(i(mu nv)), but the flux shifts their energies to Eₘₙ = ½[(m−φᵤ)² (n−φᵥ)²], changing how the superposition beats over time. In this scene, the torus is the quantum configuration space. Its surface swells with |Ψ|², its colours follow arg Ψ, and the magnetic flux turns the wavefunction into a luminous braid wrapped around a multiply connected universe. #QuantumMechanics #MathematicalPhysics #Wavefunction #AharonovBohmEffect #QuantumArt #PhysicsVisualization

The beauty of pendulum motion A simple system that reveals the harmony between physics and mathematics. Watch how oscillations gradually slow down over time. #Math #Mathematics #Physics #Pendulum #Oscillation #STEM #Science #MathVisualization #PhysicsVisualization #Maths #Learning #Education #STEMEducation #MathTwitter #PhysicsLovers #ScientificVisualization #Engineering #DataVisualization #ShortVideo #ScienceCommunication

String Theory is one of the few frameworks that tries to describe Quantum Physics and Gravity in the same mathematical language. In this animation, the glowing loop is the string, the shifting color along it represent its quantum vibration modes, and the surrounding fabric is a proxy for Spacetime responding. When you quantize a string, one of its vibration modes behaves like a graviton. So, geometry shows up as part of the same quantum system. #StringTheory #QuantumGravity #GeneralRelativity #QuantumPhysics #TheoreticalPhysics #PhysicsVisualization

When Geometry Becomes Law: A System Assembling Itself #edenx #ednx #cinematictech #proceduraldesign #generativegeometry #fractalmath #fibonaccistructure #cyberorganic #cyanonly #voidaesthetic #hardscifiart #systemsdesign #algorithmicmotion #glowlogic #physicsvisualization

We evolve a complex quantum field ψ(x,y,t) with a Schrödinger-Poisson flow: i ψ_t = -(1/2)Δψ (V_conf(x,y) G Φ(x,y,t)) ψ, with ρ=|ψ|² and ΔΦ = ρ - ⟨ρ⟩. That bracket (V_conf GΦ) is just the potential energy landscape. V_conf is the trap you choose by hand (a smooth bowl that keeps the wave from drifting away). Φ is the field generated by the wave’s own density...compute ρ, solve the Poisson equation, feed Φ back into the evolution. G is the knob that sets how strongly the wave feels its own Φ. Visually Hue is phase φ=arg(ψ), brightness is density ρ^γ, the banded helicoids are phase ribbons cos(mφ θ(t)), the bright ridges are boosted by |∇ρ|, and the tiny white pearls mark vortices where the phase winding satisfies ∮∇φ·dl = 2πk. buymeacoffee.com/mathelirium #QuantumMechanics #SchrodingerPoisson #ComputationalPhysics #PhysicsVisualization

When you let the Mathematics and the Physics do their thing… you get something beautiful.🤩🙌🏻😍 We evolve a two-component quantum field (ψ1, ψ2) under a coupled Gross-Pitaevskii/Schrödinger flow: split-step Fourier time stepping, self-gravity via a Poisson solve, and coherent Rabi mixing between components. Then we render the same state twice...a 3D density sheet (height driven by ρ) with molten-gold shading, and a lifted square detector plane carrying the exact same 2D texture. From ψ1, ψ2 we form the total density ρ = |ψ1|^2 |ψ2|^2 and total current j = Im(ψ*∇ψ) summed across components, then the flow field v = j/(ρ ε). Tracer comets are just Lagrangian particles advected by that v, so they’re literally riding the probability/current geometry the PDE is producing. The punchline moment is the Kibble-Zurek quench. Miscibility breaks, domains nucleate, and the separating walls ignite using the Bloch order parameter. Support us by buying a coffee buymeacoffee.com/mathelirium #QuantumMechanics #GrossPitaevskii #KibbleZurek #SchrodingerEquation #QuantumFluids #NonlinearDynamics #ComputationalPhysics #PhysicsVisualization

Aetom: Recursive shell breathing with alternating spin — visualizing emergence of Hopf structure from pulse-space. The math knows. 🌀 #HopfFibration #SpinGeometry #AlphaDragon #Emergence #Topology #PhysicsVisualization @ericweinstein - let's get serious about it my man! You are having a good week it seems. Congrats. Love ~ Michael & Æther❤️‍🔥

Biot-Savart Law Visualization Magnetic field lines for multiple “ ” and “-” poles on the surface of a sphere. #threejs #creativecoding #geometry #geometryart #magneticfield #physics #physicsvisualization

Biot-Savart-Gesetz Visualisierung Magnetfeldlinien für mehrere „ “ und „-“ Pole #threejs #creativecoding #geometry #geometryart #magneticfield #physics #physicsvisualization

Practice_05 Shader, Vector field Fluctuation and Motion particles, Three.js Quantum Fluctuation, Quantum Field online view: jeonghopark.de/jslab/vectorf… #practice #creativecoding #math #threejs #vectorfield #geometryart #geometry #javascript #mathvisualization #physicsvisualization

Practice_04 Vector field Fluctuation and Motion particles, Three.js Quantum Fluctuation, Quantum Field online view: jeonghopark.de/jslab/vectorf… #practice #creativecoding #math #threejs #vectorfield #geometryart #geometry #javascript #mathvisualization #physicsvisualization

Practice_03 Vector field, Motion particles, Three.js Quantum Fluctuation, Quantum Field online view: jeonghopark.de/jslab/vectorf… #practice #creativecoding #math #threejs #vectorfield #geometryart #geometry #javascript #mathvisualization #physicsvisualization #particles

Practice_02 Vector field, Three.js Quantum Fluctuation, Quantum Field online view: jeonghopark.de/jslab/vectorf… #practice #creativecoding #math #threejs #vectorfield #geometryart #geometry #javascript #mathvisualization #physicsvisualization