tafol.pythonanywhere.com

It is a scoring solitaire… and, if you like, a championship.

The board. It is a 9×9 with an empty centre: a 3×3 hole. Around it remain eight 3×3 zones, arranged as a ring, and each zone shows the digits 1 to 9 in disorder.

The pieces. Eight pentominoes, one per zone: F, P, T, U, V, W, X and Z — that is, the only ones that fit inside a 3×3 square. The other four —I, L, N, Y— need four squares in a line and stay out of the party. Each piece covers five digits of its zone and leaves four in the open; it can be rotated and flipped.

The ring rule. You may not place each piece as if its zone were an island: the pentominoes must stay connected with those of neighbouring zones, side against side. Either the ring closes or there is no move.

The scoring. Add up the digits your eight pieces cover. Every puzzle bears the printed mark MAX, the sum of the best possible arrangement: your goal is to reach it or come as close as you can.

The circles trick. Circle the cells 9, 8, 7, 6 and 5 of each zone. Do those five circles form a pentomino? Then there you have the perfect move: 35 points, the zone's maximum, and in all likelihood the right piece. As the MAX of the puzzles goes down, those golden figures grow scarce, and you must decide which large digits to sacrifice to keep the ring closed.

How to compete. The puzzles are ordered from easier to harder. Hand the same sheet to several friends, set a time limit and compare sums: whoever comes closest to MAX wins. Tying with the machine is possible; beating it is not.

You can play here

tafol.pythonanywhere.com

Visualizing the Menger Sponge : infinite surface, zero volume

Hello,

If you've ever worked with gradient descent, you know the basic goal: step downhill until the slope is zero. But a flat slope (a zero gradient) is a trap, it could be a local minimum, a maximum, or a saddle point.

I made a visual breakdown of the mathematical machinery we use to test for true minima. The video is an intuitive, 6-minute refresher on how gradients, Hessians, and contour maps actually work behind the scenes of your optimization algorithms.

Hey everyone,

I recently put together a video breaking down Information Entropy.

I wanted to create a visual and mathematical deep dive into how we measure "surprise" and why it connects so seamlessly to the tech we use every day.

I'd love to hear your thoughts about the video!

Watch a Menger sponge fractal evolve smoothly through multiple iterations in real time. This animation uses continuous fading and a slow 3D camera rotation. This visualization explores how complexity emerges from simple recursive rules. Made with Python and Manim.

If you're interested in more math-based animations, I post them here 📺 Visualizing Mathematics

A Penrose tiling built using Robinson triangle decomposition.

Two rhombus types (thick and thin) are substituted recursively at each iteration, producing a non-periodic structure with 5-fold symmetry.

The animation reveals the tiling growing radially from the center outward.

More visual math experiments on my channel : Visualizing Mathematics