Fun Animations

I enjoy animating basic concepts and here you can find some of them.

Reactive Power - Truck
This reactive power metaphor uses a truck-and-hill analogy to explain system efficiency. Active power is the useful work, shown as packages being delivered, while reactive power is the steepness of the hill, representing the wasted effort the truck must overcome.
Reactive Power - Particle Flow
This reactive power metaphor uses flowing particles to visualize electrical concepts. Useful active power is shown as blue particles moving directly to the load to perform work, while non-working reactive power is a turbulent orange or purple flow that just sloshes back and forth.
Braess’s Paradox
Braess’s Paradox is the counter-intuitive observation that removing capacity from a network, can paradoxically increase the network’s overall performance. Discovered by mathematician Dietrich Braess in 1968, this principle reveals a fundamental conflict between individual incentives and the collective good.

Polya’s Urn
This interactive tool simulates Polya’s Urn 🏺, a classic probability model demonstrating the “rich-get-richer” phenomenon. In this model, drawing a colored ball from the urn increases the probability of drawing that same color in the future. You can adjust the rules for how many balls are added after each draw and run thousands of simulations to see how early random events can dramatically shape the final outcome.
Sierpinski Triangle
This visualization demonstrates the Chaos Game, a stochastic process that beautifully generates the deterministic fractal known as the Sierpinski Triangle. The process begins with three fixed vertices and a random starting point. At each step, a new point is generated exactly halfway between the current point and a randomly selected vertex. As the process iterates, the points converge to form the intricate, self-similar structure of the fractal.
Euler’s Identity
Euler’s Identity, $e^{i\pi} + 1 = 0$, often feels like a cryptic puzzle, a gathering of mathematics’ most famous constants with no clear reason to be connected. This visualization reveals that story, showing how constant “sideways growth” (the secret of $e^{i}$) for a precise distance ($\pi$) guides a point from a starting position of 1 to a final destination of -1. Click to see the beauty behind the world’s most famous equation.