Algorithms
The Elevator Doesn't Know Where to Go. And That's the Best Algorithm We Have
Elevator dispatching is an NP-hard problem. For 60 years, the best engineers in the world have been solving it with heuristics — essentially, educated guesses.
Algorithms
Algorithms
Solving Wordle with Entropy and Excel
Can you prove mathematically that one starting word is better than another in Wordle? Yes — by treating each guess as an information query and measuring it with Shannon entropy. This article walks through the full implementation in Excel, from downloading the official word list to LAMBDA functions that compute optimal moves.
Algorithms
One Formula to Understand 3D Graphics
The entire field of 3D-to-2D projection can be understood through a single formula: x' = x/z and y' = y/z. This tutorial builds a complete 3D wireframe renderer in vanilla JavaScript using nothing but 2D Canvas, demonstrating perspective projection, rotation, and a spinning cube — with no WebGL, no Three.js, and no graphics API.
Algorithms
A Detailed Overview of Galois Fields
A comprehensive tour of Galois fields (finite fields) from mathematical foundations through practical implementation, covering their central role in AES encryption, Reed-Solomon error correction, and linear feedback shift registers. Includes C++ code for GF(2⁸) arithmetic, look-up table optimization, tower field construction, and Intel's GFNI hardware instructions.
Algorithms
Inventing JPEG
An intuitive, bottom-up explanation of the JPEG compression algorithm — from vector representations through Discrete Cosine Transform, quantization, and Huffman coding, building deep understanding without requiring prior knowledge.
Algorithms
Time Travel and Programming 2: Paradoxes
The era of time travel hasn't arrived yet, but humanity has long tried to resolve the accompanying paradoxes. We examine three models of how time responds to a traveler's actions, and conduct an experiment with a virtual time machine built on Conway's Game of Life.
Algorithms
Forging Your Signature with a Linkage Mechanism: Kempe's Theorem
A program that forges any signature using a linkage mechanism, based on Kempe's theorem from the mid-19th century — covering the mathematics of algebraic curves, Fourier series approximation, and an interactive web app.
Algorithms
Restoring Defocused and Blurred Images: Improving Quality
The final part of the image deconvolution trilogy explores Total Variation prior methods that outperform the classic Wiener filter, with an open-source implementation in SmartDeblur achieving commercial-grade quality.
Algorithms
Restoring Defocused and Motion-Blurred Images: A Practical Guide
A practical guide to image deconvolution using the Wiener filter, covering PSF acquisition, bokeh analysis, edge effects, and the open-source SmartDeblur tool that rivals commercial solutions.
Algorithms
How to Properly Sort Content Based on User Ratings
Why simple upvote-minus-downvote and average rating approaches fail, and how the Wilson score confidence interval provides the statistically correct way to rank user-rated content.
Algorithms
Real-Time Sudoku Solving with a Webcam
A deep dive into computer vision algorithms for recognizing and solving Sudoku puzzles in real time using a webcam, covering adaptive thresholding, Hough transform, OCR, and multiple solving strategies.
Algorithms
Reading QR Codes by Hand
A detailed guide on how to manually decode QR codes without a smartphone, covering the structure of QR codes, system information, masks, encoding modes, and step-by-step data extraction.