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Domain Repetition
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
Top posts
Every blog post that took off on Hacker News, ranked by the votes of its best submission. 2,391 posts.
1622
Learning Regular Languages with L* Algorithm
Research in Software Engineering from Rahul Gopinath
1623
What’s Wrong with Bayes
My problem is not just with the methods—although I do have problems with the method—but also with the ideology.
1624
Anatomy of a Lean proof for software engineers
Intro I recently worked through a problem from a theory of computation textbook that asked me to prove a property of a language using finite automata. The informal proof is a simple constructive proof where you build an automaton and show that it recognizes the language. This is kind of similar to program…
1625
Trapped priors as a basic problem of rationality
P(A|B) = [P(A)*P(B|A)]/P(B), all the rest is commentary.
1626
A Fairly Fast Fibonacci Function
A common example of recursion is the function to calculate the $n$-th Fibonacci number: def naive_fib(n): if n < 2: return n else: return naive_fib(n-1) + naive_fib(n-2) This follows the mathematical definition very closely but it’s performance is terrible: roughly $\mathcal{O}(2^n)$. This is commonly patched up with…
1627
Evolution of Random Number Generators
Prime powers have a kinda chaotic pattern in their bits. We bootstrap this idea into a good random number generator, recapitulating history.
1628
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LU Factorization and Linear Systems for Programers
Solving systems of linear equations is a staple food of linear algebra. It can be applied as a part of many machine learning tasks, although it is not always...
1630
Unicode's transliteration rules are Turing-complete
Claim: as specified, the UTS #35 transliteration-rule language is Turing-complete. This is an exception in Unicode, where algorithms are deliberately bounded and always terminate. The specification defines a revisiting cursor with no rewrite limit. ICU's implementation implements a per-call cap, but the spec itself…
1631
Four pitfalls of hill climbing
An animated look at local maxima, novelty effects, differentiation, emergent maxima.
1632
Fast Lossless Color Image Compression
In the research field of compression, the usual goal is to achieve the best possible compression rate. The best known algorithms, however, are very slow, and sometimes impractical for real-world ap…
1633
Space Emerging from Quantum Mechanics
The other day I was amused to find a quote from Einstein , in 1936, about how hard it would be to quantize gravity: “like an attempt to breathe in empty space.” Eight decades later, I think we can still agree that it’s hard.
1634
Rolling hash; Rabin-Karp string search
This is yet another string search algorithm. (Previously my readers have read about Knuth-Morris-Pratt .)
1635
Raytracing diamonds
This comes from a question posed to me and others in 2019 by Stefan Langerman, a computational geometer who also happens to be a diamond dealer. The classic ...
1636
Competitive programming in Haskell: better binary search
Binary search is a workhorse of competitive programming. There are occasional easy problems where binary search is the solution in and of itself; more often, it’s used as a primitive building block…
1637
Learning Lean: Part 1
Motivation I’ve been captivated by the recent movement to popularize mathematics formalization through the Lean theorem prover, and this year I’m diving deeper into learning it. For those unfamiliar with this revolution, I highly recommend watching Kevin Buzzard’s talks on YouTube for an overview of why formal…
1638
Simple Image Vectorization
This is an example of an image vectorization algorithm. It shows the bilinear interpolation, polynomial approximation, differential analysis, and iterative algorithms working together to solve a practical problem
1639
Singular Value Decomposition Part 2: Theorem, Proof, Algorithm
I’m just going to jump right into the definitions and rigor, so if you haven’t read the previous post motivating the singular value decomposition, go back and do that first. This post will be theorem, proof, algorithm, data. The data set we test on is a thousand-story CNN news data set. All of the data, code, and…
1640
An interactive guide to Fourier series (2022)
Drawing with the Fourier Series
1641
Tversky Neural Networks
Psychologically Plausible Deep Learning with Differentiable Tversky Similarity
1642
Faster arithmetic by flipping signs
Over the years, I picked up a number of tricks to optimize code. Today I’ll talk about one of them.
1643
Was Knuth Really Framed?
Recently, the formal methods specialist Hillel Wayne posted an interesting article discussing whether Donald Knuth was actually framed when Jon Bentley asked him to demonstrate literate programming . (Knuth came up with an 8-page long monolithic listing, whereas in a critique Doug McIlroy provided a six line shell…
1644
Parrondo's Paradox: How two ugly parents can make a beautiful baby
"How two ugly parents (mathematically) can make a beautiful baby"
1645
Math Symbols Explained with Python
Learn the meaning behind mathematical symbols used in Machine Learning using your knowledge of Python.
1646
A pair of dice which never roll 7 (2004)
Some friends of mine play the board game Settlers Of Catan . In this game, each player rolls two ordinary dice on their turn, and the number which comes up determines what resources people get for the turn. When a seven is rolled, something special happens: no resources are generated, and instead a robber moves on the…
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The inspection paradox is everywhere (2015)
I have updated this article with new data, better code, and friendlier data visualization. You can read the new version here . Th...
1649
Dark Alley Mathematics
Base changing and other calculations
1650
So You Think You Have a Power Law (2007)
Regular readers who care about such things — I think there are about three of you — will recall that I have long had a thing about just how unsound many of the claims for the presence of power law distributions in real data are, especially those made by theoretical physicists, who, with some honorable exceptions…