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Algorithms made visible.
Each reel shows an algorithm at work, step by step.
A new algorithm most days.

19,856 balls in a circle. Every k-th one steps out until one is left.

Count around the circle and the k-th ball drops out, then keep counting from the next one. The balls fall to the floor in the order they leave, so the floor turns into a rainbow. The last ball standing floats up and glows.
In daily life: sharing out turns fairly, round-robin scheduling in computers, and ring-shaped data structures.

#algorithm #josephus #math #puzzle #artandscience by @ij.muse

$40,000 balls. Each one is trying to find a root. Every ball starts on a spot and keeps making the same guess-and-improve jump, which is called Newton's method. After a few jumps it lands on one of three answers, and its color shows which one. The jagged borders between the colors never get simple, however closely you look. In daily life: calculators finding square roots, and software that solves equations in engineering and games. #algorithm #newtonsmethod #fractal #math #artandscience by @ij.muse$

$10,000 balls. One single line learns to fill a whole square. Start with a simple U shape. Then every piece of the line is replaced by a smaller U, again and again, and the line twists into a finer and finer maze. It never crosses itself, but in the end it passes near every spot of the square. In daily life: image and map databases, memory layouts in computers, and the order a printer or robot arm can visit points without long jumps. #algorithm #hilbertcurve #fractal #spacefillingcurve #artandscience by @ij.muse$

10,000 numbers. Only the primes are left standing.

Write the numbers in a spiral. Take the smallest number that is still standing, like 2, and knock down every multiple of it. Then do the same with 3, then 5, then 7, and keep going. What stays up are the primes, and they line up in strange diagonal streaks.
In daily life: the codes that protect online payments and messages rely on prime numbers.

#algorithm #primenumbers #sieve #ulamspiral #artandscience by @ij.muse

$40,000 points. Each one jumps halfway to a random corner. Pick a corner of a pyramid at random and hop halfway toward it. Do it again and again. Every ball does this on its own, yet after a few hops they all land on a pyramid made of tiny pyramids. The color shows which corner a ball hopped toward last. In daily life: random sampling in computer graphics, Monte Carlo simulations, and fractal antennas. #algorithm #chaosgame #sierpinski #fractal #artandscience by @ij.muse$

6,000 points. One rule. A butterfly made of chaos.

Every bead obeys the same three equations: dx/dt = σ(y−x), dy/dt = x(ρ−z)−y, dz/dt = xy−βz, with σ = 10, ρ = 28 and β = 8/3. At each step a bead moves a tiny bit in the direction the rule gives. There is no randomness after the start.

All 6,000 beads begin packed in a ball of radius 0.01 and travel as one clump. Then the clump stretches into a rainbow ribbon, wraps around both wings, and spreads into a cloud that keeps swirling over the whole butterfly shape. Colours show the order along the ribbon.

Edward Lorenz found this system in 1963 while studying a simplified model of air rising and sinking in the atmosphere, known as convection.

Algorithm Series · No. 14.
Explore past algorithms at @ij.muse

#algorithm #lorenzattractor #chaostheory #generativeart #artandscience by @ij.muse

$One rule, repeated. Every point either stays or escapes. This is the Escape-Time Algorithm. Each bead is one number c. Start with z = c and repeat z → z² + c. If |z| ever passes 2, the bead escapes, and the step where it escaped sets the height of the column left behind. If it stays within 2 for all 40 steps, it is treated as inside. 8,900 beads start. 2,197 stay bounded. They fly home and settle on top: the Mandelbrot set, built out of beads above terraces of escape times. Benoit Mandelbrot coined the word "fractal" in 1975 for shapes like coastlines that stay detailed at every scale. Algorithm Series · No. 13. Explore past algorithms at @ij.muse #algorithm #mandelbrot #fractal #generativeart #artandscience by @ij.muse$

$1,800 grains. One seed. No blueprint. Each grain moves randomly until it touches the growing cluster and sticks. No one draws the branches. This is a Brownian tree, formed through diffusion-limited aggregation. The result resembles branching patterns in frost, mineral deposits, and electrical discharges. Algorithm Series · No. 12. Explore past algorithms at @ij.muse #algorithm #dla #fractal #emergence #artandscience by @ij.muse$

11,000 particles. One invisible wind.

Curl Noise starts with a smooth field of directions. Taking its curl produces swirling, divergence-free motion, and the particles follow that flow.

It is used to create fluid-like motion for smoke, fire, and water in animation and games.

#algorithm #flowfield #curlnoise #generativeart #artandscience by @ij.muse

36 rows. 36 colors. One rule.

Quicksort chooses a pivot, moves smaller values to one side and larger values to the other, then repeats the process on each side until the list is sorted.

The result is the kind of ordered list you see in prices, contacts, and search results.

#algorithm #quicksort #sorting #computerscience #artandscience by @ij.muse

2,006 dots. 6 flags.

Every dot joins its nearest flag. Every flag moves to the middle of its dots. Repeat, and the crowd sorts itself into groups.
In daily life: how shops group customers, how photo apps shrink thousands of colors down to a few.

Algorithm Series · No. 9.
Explore past algorithms at @ij.muse
#algorithm #kmeans #clustering #machinelearning #artandscience by @ij.muse

Follow the slope. Reduce the error.

Gradient descent checks the slope at the current position, takes a step downhill, then checks again. The learning rate controls the size of each step. Too large, and it can overshoot. Too small, and progress slows. Different starting points can lead to different valleys.
In daily life: training models to recognize speech, filter spam and recommend music.

Algorithm Series · No. 8.
Explore past algorithms at @ij.muse
#algorithm #gradientdescent #optimization #machinelearning #mathvisualization by @ij.muse

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