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Avoiding Trigonometry (2013)
Tutorials and articles of Inigo Quilez on computer graphics, fractals, math, art, demoscene, shaders and more.
Most cited
Posts that commenters keep linking to, ranked by how many different people have cited them in Hacker News comments. 417 posts.
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Cargo Cult Quantum Factoring
Just days after we celebrated my wife’s 40th birthday, she came down with COVID, meaning she’s been isolating and I’ve been spending almost all my time dealing with our kids. But …
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The Missing 11th of the Month (2015)
Personal website of David R Hagen, scientific software engineer
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Diffusion Is Spectral Autoregression
A deep dive into spectral analysis of diffusion models of images, revealing how they implicitly perform a form of autoregression in the frequency domain.
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An Introduction to Cache-Oblivious Data Structures
If you read my recent post about Postgres you may have noted that Postgres operates primarily with fixed-size blocks of memory called “pages.” By default, Postgres pages are 8KB. This number is tuned to match operating system page sizes which are tuned to match hardware cache sizes. If you were to run Postgres on…
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Mapping the internet with Hilbert curves
The internet is big. Really big . You just won’t believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think the /22 you got as a LIR was big, but that’s just peanuts to the internet.
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Infinite Grid of Resistors
There is a well-known puzzle based on the premise of an �infinite� grid of resistors connecting adjacent nodes of a square lattice. A small portion of such a grid is illustrated below.
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Euler's Fizzbuzz (2020)
FizzBuzz is a common coding problem asked in technical screenings or interviews. It goes something like this:
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The Beauty of Roots (2011)
Around 2006, my friend Dan Christensen created a fascinating picture of all the roots of all polynomials of degree ≤ 5 with integer coefficients ranging from -4 to 4:
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GPT-4 gets a B on my quantum computing final exam
Update (April 14): On the suggestion of my TA Justin Yirka, I gave GPT-4 problem 2 from the final exam, along with its own answers and my and Justin’s grading comments, and asked it whether i…
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Gridlock vs. Bottlenecks: A visual explanation
"Emails show [Chris Cristie]'s aides did plan bridge gridlock," says Salon . To a transportation engineer, the aides are innocent: bridges can't have gridlock. While we often say "gridlock" to mean "bad traffic," it has a technical meaning.
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Faster remainders when the divisor is a constant: beating compilers & libdivide
Not all instructions on modern processors cost the same. Additions and subtractions are cheaper than multiplications which are themselves cheaper than divisions. For this reason, compilers frequently replace division instructions by multiplications. Roughly speaking, it works in this manner. Suppose that you want to…
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How Far Can You Get From McDonald's?
This summer, cruising down the I-5 through California’s Central Valley to the Los Angeles Basin, I unwittingly stumbled upon a most exasperating development: the country strip mall . First, let me state that I don’t hate. I’ve got nothing against Petco, Starbucks, OfficeMax, et al. When overcome by the desire for a…
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Monte-Carlo Simulations
Monte Carlo simulations (or methods ) is the technique of applying randomness and the Law of large numbers to the solution of various scientific and engineering problems. One of its first documented uses was by Stanislaw Ulam and John von Neumann for nuclear weapon simulations after WWII [1] .
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The strange story of “Extended Random”
Yesterday, David Benjamin posted a pretty esoteric note on the IETF’s TLS mailing list. At a superficial level, the post describes some seizure-inducingly boring flaws in older Canon printers…
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Patent 5,893,120 reduced to mathematical formulae
I have previously argued that the Bilski ruling renders all software unpatentable in the US because any method of manipulating information ...
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The Prime That Wasn’t
Life, technology, and other good things
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Neural Networks Are Essentially Polynomial Regression (2018)
You may be interested in my new arXiv paper, joint work with Xi Cheng, an undergraduate at UC Davis (now heading to Cornell for grad school); Bohdan Khomtchouk, a post doc in biology at Stanford; a…
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Double encryption: Analyzing the NSA/GCHQ arguments against hybrids
In 2019, Google and Cloudflare ran an experiment where they upgraded HTTPS for many "real users’ connections" to use post-quantum encryption. They then reported statistics on how affordable this was. Google had also run a similar experiment in 2016: "While it's still very early days for quantum computers, we're…
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A reasonably speedy Python ray tracer
Cyrille Rossant's small ray-tracer is an nice self-contained Python program (using NumPy) that renders this 400×300 image in about 15 seconds on a fast PC:
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Comparing City Street Orientations
This post is adapted from this research paper that you can read/cite for more info. It analyzes and visualizes 100 cities around the world.
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Lovelace's Leap
There's a great deal said about Ada, Countess of Lovelace that I find misguided. And, worse, the real intellectual triumph of Lovelace is ...
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Sunset Geometry (2016)
Robert Vanderbei has written a beautiful series of articles and talks about a method for finding the radius of the earth based on a single photograph of a sunset over a large, calm lake.