#Python Set Intersection

🌐 Lissajous Curve animation equation #maths #mathematics #usa #codematrixvishal #lissajous

The gradient is one of the core ideas in multivariable calculus. In this animation, I explain its geometric meaning and why it always points in the direction of maximum increase. We connect partial derivatives, direction, and 3D surfaces to build real intuition. The gradient is not just computation — it describes how functions change in space. Essential for engineering, physics, and data science. Share it with someone studying vector calculus 👇 #VectorCalculus #Gradient #MultivariableCalculus #STEMEducation #EngineeringMath

Curlicue curves are fascinating geometric paths created by repeatedly adding tiny complex-number steps, one after another. In this animation, the curve is generated by an iterative rule of the form z(n+1) = z(n) + step(n, t), where each new point depends on the previous one. The step itself is a rotating complex number whose direction is controlled by an exponential with an imaginary argument, and whose size slowly changes with n. The angle of each step is not random. It is driven by trigonometric functions involving both the iteration index n and a continuous time parameter t. As t changes, the direction of the steps oscillates, producing smooth curls, loops, and dense spiral structures. This is why the curve looks organic and fractal-like, even though it is fully deterministic. Because the curve is built from thousands of small additions, local patterns repeat at different scales, a key idea behind fractals. At the same time, the gradual decay in step size keeps the curve bounded and visually coherent. Curlicue curves like this connect complex numbers, iteration, trigonometry, and geometry in a single visual process, showing how rich structure can emerge from a simple mathematical rule.

Intuitive visualization of the gradient in multivariable calculus. The curves show equal values of the function. Moving along them does not change height. The gradient points across those curves in the fastest way. That means: it gives the maximum increase. Any other direction grows slower. A simple idea shown visually. #calculus #gradient #multivariable #vectors #math

visualizing calculus. finding the roots of z^3 - 1 = 0 on the complex plane, zooming straight into the origin where the math completely breaks down.#calculus #fractals #complexmath #mathart #programming

This is what ∫ actually means 🤯 Slice a curve into rectangles. More rectangles → better fit. Infinite rectangles → EXACT area. That’s integration. That’s all it is. ✨ 📐 Axiom Motion — Mathematics Visualized #math #calculus #integration #integral #mathanimation

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."

Lissajous machines are mechanical devices designed to physically trace Lissajous curves using coupled oscillatory motion. Typically, they rely on two perpendicular harmonic motions—often produced by rotating cams, gears, or pendulums—where each motion has its own frequency, amplitude, and phase. As a pen or stylus is attached to the moving mechanism, the combined motions generate intricate looping patterns on paper or a drawing surface. By adjusting gear ratios or linkage lengths, the machine can smoothly transition between simple ellipses and highly complex woven figures. What makes Lissajous machines fascinating is that they turn abstract trigonometric relationships into something tangible and visual. Each curve directly reflects the ratio of frequencies and the phase difference between the two oscillations, so the drawing becomes a physical record of harmonic motion. Historically, these machines were both scientific tools and artistic instruments, used to study vibration, resonance, and periodic motion long before digital plotting existed. Even today, they sit beautifully at the intersection of mathematics, physics, and mechanical art, showing how precise motion can produce surprisingly elegant structure. Like and follow @mathswithmuza for more! #math #machine #algebra #calculus #foryou

Curling 🥌. #vector #calculus #math #geometry #topology

The School of Futuristic Intelligence (SFI) This mathematical animation is an exhibition of spherical harmonics. Coded in JavaScript using Three.js, with custom GLSL shaders. These programming languages leverage the power of parallel processing on the GPU to produce the metallic effect and the high-precision, high-vertex geometry of the object. Learn more about Enlightened Mathematics and Mathematical Coding at The School of Futuristic Intelligence. Link in the bio.

Polar coordinates (r,θ) are essential for modeling systems with circular symmetry, rotation, or direction-based data. E.g. navigation 🧭, robotics, data analysis and modelling, nature & biology. #geometry #naturelovers #math #graphics #desmos

Wait for the drop when c hits the sweet spot. 👁️👇 This is the Julia Set. It’s a map of infinite chaos generated by one simple rule: take a number, square it, and add a constant. Over and over again. 🎨 What do the colors mean? They are a speedometer for infinity. • Black: The "Prisoners." These numbers are trapped in the loop forever. They never escape. • Neon/Color: The "Escapers." The color tells you exactly how fast that pixel exploded to infinity. • Red/Hot: Escaped instantly. • Blue/Cool: Tried to stay trapped but lost the battle. Mathematical art at 60FPS. 🐍✨ #juliaset #math #fractal #python #coding