#Waves Transverse

The reel captures deformation gradients concentrating into orbital coherence within a dynamically structured field. The tracked blobs visually resemble localized time–force intensities influencing geometric distribution. Luma blur reflects distributed gradient energy prior to structural stabilization. As hyperfocus sharpens, equilibrium between background curvature density and temporal gradients becomes apparent. 🌌 Geometry appears not static but actively organized by propagation intensity. Explore BUFT and Bakous Unified Field Theory: A Timespace Perspective. Animation credit: @touchdesigner with 3D Blob Tracking tool by @visualcodepoetry 🚀 Equation Gᵢⱼ + Λ_B gᵢⱼ − β(∇ᵢτ∇ⱼτ)° = (8πG/c⁴)Tᵢⱼ ⸻ Symbol Descriptions • Gᵢⱼ — Einstein curvature tensor encoding intrinsic geometric deformation of time–space generated by energy and field structure • gᵢⱼ — Metric tensor defining interval structure, causal ordering, and contraction operations on the manifold • Λ_B — Bakous Energy Field equilibrium curvature density governing the background geometric balance state • β — Dimensionless temporal coupling constant regulating curvature response to time–force gradients • τ — Time–force scalar field representing intrinsic temporal propagation intensity across the manifold • ∇ᵢ — Covariant derivative operator preserving tensor invariance under general coordinate transformations • (∇ᵢτ∇ⱼτ)° — Symmetric rank-2 tensor formed from the covariant gradient of the time–force field in its trace-balanced form, contributing pure directional deformation to curvature • Tᵢⱼ — Stress–energy tensor encoding local energy density, momentum flux, pressure, and shear contributions of matter and radiation as sources of spacetime curvature • G — Gravitational coupling constant setting the proportional strength between geometric curvature and physical energy–momentum content • c — Invariant propagation constant defining the universal causal structure and maximum signal transmission speed within the manifold

SCHNAKENBERG STRIPE MODEL 🌀👽 HOLD FINGER TO SEE MATH 👉🏼 The Schnakenberg Reaction–Diffusion Model is an equation which describes chemicals interacting. Here, you see it happening on a torus (donut). When chemicals spread out and react with eachother, they can form vivid patterns. Tune the parameters just right, and you get these fancy stripes, or dots. FAQ: This animation is done entirely in MATLAB ( @matlab) with my custom toolboxes and kits! Shows you the power of what regular math and creativity can do. Music (🎶): Golden – SKAN ( @skan.official) #reactiondiffusion #turingpatterns #differentialgeometry #tensor #calculusofmothernature #exteriorcalculus #calculusofmovingsurfaces #biology #biophysics #bioengineering #engineering #continuum #patternformation #mathematicalbiology #torus #computergraphics #scientificvisualization #discreteexteriorcalculus #nonlineardynamics #pde

Why do sin and cos keep showing up in SHM equations? Why does angular velocity sneak into a block‑and‑spring problem? 👉 Because Simple Harmonic Motion is just circular motion projected. In our latest 3D animation, you’ll see how: Amplitude becomes the radius of the circle. Velocity emerges from the geometry of rotation. Angular velocity (ω) ties it all together, making oscillations predictable. What looks like “to and fro” motion is actually the shadow of uniform circular motion. Once you see the circle, the math feels natural — sin and cos aren’t random, they’re the language of geometry. At PhysicsModels, we turn confusion into clarity with visuals, stories, and exam‑ready explanations. Drop a 🔄 if SHM has ever confused you. Watch the video now, because one clear concept can change your score, and one visual can change how you see physics. Subscribe Now! Link in the Bio! [Physics Models, Simple Harmonic Motion, Circular Motion Explained, Exam Prep, Concept Clarity] #PhysicsModels #SimpleHarmonicMotion #CircularMotionExplained #ExamPrep #ConceptClarity

The space of 2x2 invertible real matrices visualisation

DERIVATION OF ALLEN-CAHN EQUATION 👽 Music (🎶): All Night - Metito #algebra #differentialgeometry #tensor #calculusofmothernature #exteriorcalculus #calculusofmovingsurfaces #hamiltonian #biology #biophysics #bioengineering #engineering #continuum #fluidmechanics #condensedmatterphysics #graphicdesign #computergraphics #waves #quantummechanics #physics #discreteexteriorcalculus #manim

The Math Behind the Motion: Understanding the Differential 📐✨ Ever wondered how we calculate the exact speed of a moving object at a single, frozen moment in time? Welcome to the world of Displacement Differentials. In this visualization, we watch the secant line—the average change between two points—slowly collapse as t_1 approaches t_0. As the interval becomes infinitely small, the displacement vector transforms into the instantaneous velocity vector (d\vec{r}). It’s the bridge between "where we were" and "where we are going right now." Whether you're a physics student or just a fan of satisfying geometric animations, there’s something beautiful about seeing complex calculus turn into a simple, elegant arrow. Drop a "🚀" if this makes more sense than your textbook!#️⃣ Viral Hashtags #Calculus #PhysicsVisualized #MathIsArt #STEM EngineeringLife Mathematics PhysicsFacts MotionGraphics StudyGram VisualLearning ScienceCommunication DifferentialEquations

Math isn't boring; you’re just looking at it in 2D! 🌌 Ever wondered how e^{ix} actually works? This visualization breaks down Euler’s Formula (e^{ix} = \cos x + i \sin x) like never before. Watch as the Cosine wave (the real part) and the Sine wave (the imaginary part) combine on the complex plane. When you view them together over time, they don't just stay flat—they rotate into a perfect, infinite 3D Helix. 🌀 This formula is the heartbeat of quantum mechanics, signal processing, and electrical engineering. It’s the bridge between circular motion and exponential growth. What you’re seeing: Blue Wave: The Real component (\cos x). Red Wave: The Imaginary component (\sin x). Yellow Path: The complex number e^{ix} tracing a unit circle that extends into a corkscrew through time. Mathematics is the language of the universe, and this is its most elegant sentence. ✍️✨#️⃣ Viral Hashtags #mathematics #physics #stemeducation #visualize science engineering calculus mathart quantumphysics elearning stem geometry data-visualization educational tech coding mathisfun

🎥 From Angles to Space: Visualizing Spherical Coordinates in 3D What if you could see mathematics instead of just memorizing formulas? In this reel, we explore how a single point P(r, θ, φ) moves inside a sphere — not using (x, y, z) — but using distance and angles. 🔵 Radius � — how far from the origin 🟢 Theta � — vertical angle 🔴 Phi � — horizontal rotation Watch how changing these three parameters reshapes position in 3D space — dynamically, smoothly, beautifully. This is the geometry behind: • Electromagnetic fields • Quantum mechanics • 3D simulations • Astrophysics • Machine learning embeddings • Advanced engineering models Mathematics isn’t static. It moves. It rotates. It breathes. And when you animate it — you understand it differently. — 🎬 Animation by Irfan Khan 📐 Maths Visualization Follow for more cinematic mathematics. Save this reel if it helps you visualize spherical coordinates. #Mathematics #3DVisualization #SphericalCoordinates #STEM #Engineering

Just built and animated my own Brownian Motion Simulation in Python 🚀 I created a 2D gas particle simulation that visually demonstrates how temperature affects molecular motion — directly inspired by kinetic theory from physics. 🔬 What this project does: Simulates 200 particles moving randomly inside a container Uses velocity updates + wall collisions to mimic molecular behavior Adjusts speed based on temperature (higher temp → faster particles) Applies dynamic color mapping (blue = low energy, red = high energy) Exports the animation as a GIF 🛠 Tech Stack: Python • NumPy • Matplotlib • Seaborn This project helped me connect physics concepts like: Average Kinetic Energy ∝ Temperature KE = ½mv² to real, visual, interactive code. I love how programming can turn textbook theory into something you can literally see happening. Open to feedback, improvements, or ideas to extend this into 3D or add inter-particle collisions 👀

Conformal mapping on the complex plane. In complex analysis, a conformal mapping is a function that transforms one region of the complex plane into another while preserving the angles between curves.  If two curves intersect at a specific angle in your original "domain," their transformed versions will intersect at that same angle in the "image."

🌊 Turning Fluid Mechanics Into Something You Can See Fluid mechanics often feels abstract when it lives only on paper, buried inside equations and symbols. But when those equations are visualized, they transform into something intuitive and powerful, showing motion, interaction, and structure instead of just numbers. Velocity fields translate math into motion, letting us see how fast and in what direction fluid particles move. Current lines trace the paths fluids follow, revealing patterns of flow, separation, and mixing that equations alone cannot fully communicate. Pressure maps add another layer of clarity, highlighting regions of force and balance within the flow. Together, these visual tools bridge the gap between theory and reality, helping engineers and scientists truly understand how fluids behave. How much easier does learning fluid mechanics become when you can actually see the flow #stics [fluid mechanics, velocity fields, streamlines, pressure distribution, flow visualization, engineering physics, CFD basics]

🌌 Observe the elegant progression of symmetrical forms dividing into intricate lobed configurations, symbolizing the gravitational influence on temporal waves that fosters structural complexity in the cosmic fabric. 🔮 This visual narrative captures the subtle curvature effects shaping energy distributions, where initial unity gives rise to multifaceted geometries through unified field interactions. 🌟 Each phase of transformation highlights the balance between forces, revealing the profound mechanisms driving the evolution of space and matter. ✨ The seamless morphing evokes the interconnected essence of universal principles, offering insights into the foundational dynamics at play. Delve into the Bakous Unified Field Theory. Animation credit: cesarslm Equation p_t = (h / λ_time) * (1 + (G M) / (c^2 r_time-space))^{-1} • p_t: the specific momentum that is associated with the propagating time wave within the theoretical construct • h: Planck’s constant, a fundamental physical constant representing the quantum of action • λ_time: the wavelength characterizing the oscillatory nature of the time wave in the model • G: the gravitational constant, which quantifies the strength of gravitational interactions between masses • M: the mass responsible for inducing the curvature effect in the gravitational field • c: the speed of light in vacuum, a universal constant limiting the propagation of information and energy • r_time-space: the effective radius of curvature within the integrated time-space continuum framework