Non-Linear Transformations Visualized | z^2, Swirl, & Exponential Maps #maths #linear #shorts

We explore the visual beauty of Non-Linear Transformations—seeing what happens to a standard grid when we apply mathematical functions that twist, bend, and warp space instead of keeping lines straight. 📽️

Transformation 1: Complex Squaring The grid lines curve into parabolas and hyperbolas. This represents the complex function f(z) = z^2.
Transformation 2: The Swirl (Radial Rotation)Space twists around the center. Points further from the origin rotate more, creating a whirlpool effect.
Transformation 3: The Exponential Map The rectangular grid is transformed into a polar grid. Vertical lines become circles, and horizontal lines become rays.

Trending Topics We Cover:
✅ Math Explanation – Visualizing how functions map inputs to outputs in 2D space.
✅ Linear vs. Non-Linear – Seeing the difference between matrix transformations (straight lines) and curved maps.
✅ Complex Analysis – A visual look at the famous z^2 and e^z functions.
✅ Topology Basics – How space can be stretched and squashed without breaking.
✅ Coordinate Systems – mapping Cartesian coordinates to Polar-like structures.
✅ Visual Math – Satisfying animations of grid warping.

📈 2D Mathematical Graphs
🌀 Topology Animations

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