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Tetris is capable of universal computation
This text presents a method for embedding a programmable, general-purpose, digital computer into Tetris. It describes the capabilities and performance of an implementation that runs Tetris on Tetris.
Topics /
Math & Algorithms
The most popular blog posts about math & algorithms on Hacker News. 221 posts.
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Modern Image Processing Algorithms Implementation in C
Learn how modern image analysis and processing algorithms works under the hood with their C/C++ implementation on PixLab's APIs & FACEIO, facial recognition framework using the SOD Embedded Computer Vision Library.
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They say that stocks go down during the day and up at night
Prompted by your blog post this morning, I attach a plot from Figure 3 of They Still Haven’t Told You showing overnight and intraday returns to AIG (with logarithmic vertical scale, updated with data through the end of October).
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Sub-pixel distance transform
High quality font rendering for WebGPU
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Beyond automatic differentiation
Posted by Matthew Streeter, Software Engineer, Google Research Derivatives play a central role in optimization and machine learning. By locally app...
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Fusion Foolery
Great. The fusion hype is bad enough already. Now its resurgence is going to interrupt the series of posts I’m in the middle of publishing in order for this post to be “timely.”
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A trick to eliminate 2π (sometimes)
As a physicist, I’ve learned that the presence of 2 π 2\pi 2 π [▼] [ Or rather τ \tau τ , as it should actually be called . ] in a formula usually spells trouble. It’s kind of annoying to write by hand, easy to forget, and it’s dimensionless, so you can’t easily check if you forgot to divide or multiply by it…
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Can a Rubik's Cube be brute-forced?
a personal blog
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My favorite prime number generator
Many years ago I've re-posted a Stack Overflow answer with Python code for a terse prime sieve function that generates a potentially infinite sequence of prime numbers ("potentially" because it will run out of memory eventually). Since then, I've used this code many times - mostly because it's short and clear. In this…
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How large is that number in the Law of Large Numbers?
All large numbers are large, but some are larger than others
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Two algorithms for randomly generating aperiodic tilings
[Part of a series: Penrose and hats | Spectres | finite-state transducers | more transducers | refining tilings ]
102
The Smallest Hash Table
This December I once again did the Advent of Code , in Rust. If you are interested, my solutions are on Github. I wanted to highlight one particular solution to the day 2 problem as it is both optimized completely beyond the point of reason yet contains a useful technique. For simplicity we’re only going to do part 1…
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Role of Algorithms
This is lobste.rs comment as an article, so expect even more abysmal editing than usual.
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A new line drawing method for the cycle savvy
In the demoscene, there's never a boundary that can't be pushed. My recent 4k demo "Boo!" ( YouTube ), released at X 2023, is a humble attempt to contribute to this ongoing evolution. In particular, it pioneers a new way of computing lines.
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Reflected Diffusion Models
Diffusion models are trained to reverse a stochastic process through score matching. However, a lot of diffusion models rely on a small but critical implementation detail called thresholding. Thresholding projects the sampling process to the data support after each discretized diffusion step, stabilizing generation at…
107
We're Knot Friends
It’s April Cools again. For a few summers in high school and undergrad, I was a day camp counselor. I’ve written before about how it helped me develop storytelling skills, but recently I thought of it again because, while I was cleaning out a closet full of old junk, I happened upon a bag of embroidery thread. While…
108
A baffling scale transform on a chart of university course selection trends
Harvard Magazine printed the following chart that confirms a trend in undergraduate majors that we all know about: students are favoring STEM majors at the expense of humanities.
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A mathematical formalization of dimensional analysis (2012)
Mathematicians study a variety of different mathematical structures, but perhaps the structures that are most commonly associated with mathematics are the number systems, such as the integers $late…
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Basic math related to computation and memory usage for transformers
We present basic math related to computation and memory usage for transformers
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Bitwise Division
Integer division is expensive. Much more expensive than multiplication. Much, much more expensive than addition. If you’re trying to make some integer operations really fast it’s bad news if you need to do division.
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LHC experiments see first evidence of a rare Higgs boson decay
The discovery of the Higgs boson at CERN’s Large Hadron Collider (LHC) in 2012 marked a significant milestone in particle physics. Since then, the ATLAS and CMS collaborations have been diligently investigating the properties of this unique particle and searching to establish the different ways in which it is produced…
113
Every factorial approximates a power
For every n, there is a base b such that n! = b^n. The relation between n and b(n) is surprisingly close to linear.
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Bézier Curves and the logic behind them
The logic behind Bézier Curves used in CSS animations and visual elements.
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Lindenmayer systems
A Lindemayer system or LSystem for short consists of an alphabet of symbols that can be used to make strings, a collection of production that expand each symbol into some larger string of symbols, an initial “axiom” string from which to begin construction, and a mechanism for translating the generated strings into…
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The Fibonacci Matrix
When you think about the Fibonacci sequence, you probably imagine a swirling vortex of oscillating points stretching outwards to infinity: Okay, no, obviously you don’t. Yet.
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Simple Pathtracing (2012)
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
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A linear algebra trick for computing Fibonacci numbers fast
Fast Fibonacci Computations With a Linear Algebra Twist
119
Lean, Coq and other proof assistants: Visualising proofs as trees
This week we (me & Anton Kovsharov) published Paperproof, a Gentzen-tree-like proof interface for Lean 4. In this post I'll review proof visualisations from o...
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C.R. Rao: A Life in Statistics (2020)
Presently into the 100th year of his life of vast experience, living in his Buffalo residence, here is a video message communicated by his daughter when he turned 99, at the beginning of a year-long celebration, with conferences in his honour at various places.