NIKHEDONIA
Mathematics · Algorithms · Engineering
Distributed Systems··13 min read
Raft: Consensus, Visualized
An interactive deep-dive into the Raft consensus algorithm — leader election, log replication, snapshots and truncation — with two live simulations you can explore and break.
Also In This Issue
The Abelian Sandpile: A Group Hiding in a Pile of Sand
The Bak–Tang–Wiesenfeld sandpile model (ASM) is a deceptively simple cellular automaton that conceals a rich algebraic structure — an abelian group whose identity element is a non-trivial fractal-like configuration.
Automatic Differentiation
A deep-dive into automatic differentiation: symbolic vs. numerical vs. AD, AST transformation, dual numbers, tapes, hybrid methods, and a generic C++ implementation that computes gradients and solves optimisation problems.
Detecting Hallucinations in LLM Summaries
LLMs write convincingly but fabricate facts. A practical tour of automated detection techniques: BERTScore, embedding similarity, ROUGE/n-gram overlap, NER-based cross-referencing, and QAEVAL.
◆ Interactive Feature
Conformal Maps: When Complex Functions Preserve Angles
A conformal map preserves angles: near every point it behaves like a rotation followed by a uniform scaling. Explore them in a playground that warps grids and images — written with complex numbers, 2D vectors, and dual numbers.
Read full article →Interactive Features
Conformal Maps: When Complex Functions Preserve Angles
A conformal map preserves angles: near every point it behaves like a rotation followed by a uniform scaling. Explore them in a playground that warps grids and images — written with complex numbers, 2D vectors, and dual numbers.
15 min readEML: One Operator Is All You Need
How a single binary operator — eml(x,y) = exp(x) − ln(y) — can generate every elementary function a scientific calculator knows, from addition to trigonometry.
9 min readThe Challenges of WebGL
WebGL lets you run shaders in the browser — and that's genuinely magical. But using it for arbitrary GPU computation quickly reveals a thicket of constraints that OpenCL and WebGPU were designed to escape.
12 min readModern Portfolio Theory and the Efficient Frontier
Markowitz's mean-variance framework in one picture: why correlation, not just volatility, determines what a portfolio can achieve — and why the frontier is a map, not a money machine.
10 min readShannon's Demon: Volatility Harvesting and the Loss Bias of Leverage
A fair coin that moves ±10% a round already loses 0.5% a round. Rebalancing half against cash cuts that loss; a small edge turns it into a positive harvest. The same arithmetic explains why leveraged ETFs bleed.
9 min readThe Kelly Criterion: How Much to Bet When You Have an Edge
Sixty-one finance professionals, a coin that lands heads 60% of the time, and a formula for bet sizing. Why maximizing expected value can bankrupt you, why 20% beats 40%, and why most professionals bet half Kelly.
10 min readThe Order Book: How Price is Actually Born
A hands-on look at how a limit order book works — matching engines, price discovery, support and resistance zones — with a live simulation you can drive yourself.
9 min readGenerating Fake Stock Charts: From Random Walks to Order Books
A deep dive into synthetic stock price generation — from naive coin-flip random walks, through Gaussian distributions and fat tails, to a simulated order book — and how candlestick pattern analysis reveals the gap between each model and reality.
16 min read◆ Interactive Feature
The Bertrand Paradox: When Randomness Needs a Definition
A deceptively simple question — what is the probability that a random chord of a circle is longer than the side of its inscribed equilateral triangle? — has three different correct answers depending on what 'random' means.
Read full article →More Interactive Features
The Bertrand Paradox: When Randomness Needs a Definition
A deceptively simple question — what is the probability that a random chord of a circle is longer than the side of its inscribed equilateral triangle? — has three different correct answers depending on what 'random' means.
6 min readWhy Tuning a Piano is Mathematically Impossible
Perfect harmony is a mathematical impossibility. Here's the beautiful, maddening reason why — and how piano tuners have learned to live with it.
9 min readFrom Regex to Automata to Generators
How regular expressions compile to deterministic finite automata — with an interactive visualizer, a DFA-powered string generator, and a note on closing the loop with property-based testing.
9 min readThe Fourier Transform: From Sines to Signals
A visual and mathematical journey through one of the most beautiful ideas in all of mathematics — decomposing any signal into its frequency components.
3 min readReact vs SolidJS: Dynamic Graphs, Static Graphs, and the Price of Flexibility
React and SolidJS share JSX syntax but are built on fundamentally different computational models. Understanding why illuminates a much older tension in functional programming — and an eerily similar split that once divided PyTorch from TensorFlow.
9 min readFuzzy Search: Typos, Tries, and the Algorithms Behind Instant Results
A deep dive into how fuzzy search works — from edit distance and tries to stemming, BK-trees, and how Lucene/Elasticsearch find typo-tolerant matches at scale.
11 min readPerfect Hash Functions: Collision-Free by Design
A deep dive into perfect hash functions — what they are, why they matter, how to find one efficiently with parallel search, and how they compare to JavaScript's built-in Map.
8 min readFrom DIY Monorepo to Nx: Lessons from a White-Label Credit Card Platform (2024)
Part 2 of a multi-year migration case study. After building a homegrown monorepo toolchain, we adopted Nx — and discovered that its opinionated approach solves some problems elegantly while creating new ones when your apps can't truly be isolated.
11 min read
A turn-based game born from pen-and-paper lectures. Draw lines to move the ball into your opponent's goal — bouncing off walls and previous lines makes every match more chaotic than the last.
A pipe-rotation puzzle inspired by graph theory. Connect all sources to all sinks by rotating segments. Puzzles are procedurally generated via a maze-like algorithm.
Matrix inversion in disguise. Reduce the grid to the identity using elementary row operations — without realising you're doing linear algebra.
From Legacy to Monorepo: Migrating a White-Label Credit Card Platform (2021–2024)
A four-year case study of migrating a white-labeled credit card platform from a legacy Angular/C# stack to a React monorepo with single-spa — covering GraphQL BFFs, micro-frontends, build parallelization, and the people problems that matter more than the tech ones.
Optimizing CI Builds with Docker Layer Caching on TeamCity
How we cut build times from 45 minutes down to 3–10 minutes on an on-premise TeamCity cluster using multistage Docker builds, content-addressed cache keys, and shared filesystem volumes — plus what modern BuildKit unlocks today.
buckaroo.pm - Find C++ packages
A companion website for the Buckaroo package manager — browse ~400 C++ packages from GitHub, explore the dependency graph, and find what you need instantly with precompiled fuzzy search.