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The blog at the bottom of the sea
Personal blog · blog.demofox.org · on HN as Atrix256programminggamesmath
The blog at the bottom of the sea is a personal blog at blog.demofox.org about programming, games and math. Since 2015, 55 different Hacker News readers have linked it 149 times, most often “When random numbers are too random: Low discrepancy sequences (2017)”. It is still writing: the last post was on 2026-10-24, and you can follow it by feed.
Too few sampled comments (19) to say how often HN recommends it.?
Why HN links it
HN readers link this blog's posts on automatic differentiation with dual numbers, path tracing, blue noise and low-discrepancy sampling. Most comments cite them for explanations; a few praise them.
- Recommended for · 4 comments
- Described as a "quick intro" worth a look; the path tracing part 1 post is called a source of relief for a terminology pet peeve; enjoyed for the dual-numbers a
Summarised by Claude from a sample of 19 HN comments that link here. Each comment is marked recommending, critical or neutral (citing without judging); how this works.
Most Recent Posts:2026-10-24 Why The Concept of Data Poisoning Annoys Me2026-10-15 Binary Serialization in df_game_data2026-10-07 Why The AI Determinism Argument Annoys Me2026-10-03 The Double Headed Stack Allocator2026-07-01 What To Learn To Be A Real Time Graphics Programmer2026-05-19 My Professio
Most-linked posts?
- When random numbers are too random: Low discrepancy sequences (2017)4 people · 4 mentions · first linked 2017-05-29
- Using Wang Tiles to Simulate Turing Machines4 people · 4 mentions · first linked 2020-01-21
- Generating Blue Noise Sample Points with Mitchell’s Best Candidate Algorithm4 people · 4 mentions · first linked 2017-10-20
- /2014/12/30/dual-numbers-automatic-differentiation/3 people · 6 mentions · first linked 2019-03-07
- Interleaved Gradient Noise: A Different Kind of Low Discrepancy Sequence3 people · 3 mentions · first linked 2022-01-01
- Monte Carlo Integration in 1D3 people · 3 mentions · first linked 2018-06-13
- Dissecting "Tiny Clouds" shadertoy (2017)3 people · 3 mentions · first linked 2017-11-26
- Interpolating Data over Arbitrary Shapes with Laplace’s Equation3 people · 3 mentions · first linked 2020-10-13
- Multivariable Dual Numbers and Automatic Differentiation2 people · 3 mentions · first linked 2017-02-20
- Solving N Equations and N Unknowns: The Fine Print (Gauss Jordan Elimination)2 people · 2 mentions · first linked 2017-04-10
What Hacker News says?
If I understand you correctly, I think you missed my point. You're explaining how with true randomness, you get different stuff most of the time and the same stuff some of the time. That is true. But it's not what people want when they press shuffle. What people want is something _different_, and giving the same song twice is not something different. As another commenter wrote, giving multiple (different) songs afte…
Comment linking /2017/10/20/generating-blue-noise-sample-points-with-mitchells-best-candidate-algorithm/
on “We think this cool study we found is flawed. Help us reproduce it”Submitted Derivatives, Gradients, Jacobians and Hessians as a story · 280 points
HN discussionHere are a bunch of blogs from my RSS reader that I think are worth reading. Some of them haven't updated in a while, but the archives may be worth a look anyway. * Blogs with a math focus: http://blog.sigfpe.com http://bit-player.org http://mathr.co.uk/blog/ https://www.johndcook.com/blog/ * Blogs with a programming languages focus: https://existentialtype.wordpress.com https://bluishcoder.co.nz http://blog.ezyang.…
Comment linking /
on “Ask HN: What programming blogs do you follow?”Submitted Why can’t you design noise in frequency space? as a story · 164 points
HN discussionThis link[0] has an example; so basically almost anything in a game where it has to lookup massive amounts of data (e.g. logs), the example in the article is to quickly check if the user has already seen an item (in a game with thousands of items [e.g because those were pseudo-randomly generated, think RPGs]). But it's easy to think further applications: quickly check if the player already played this chess game bef…
Comment linking /2015/02/08/estimating-set-membership-with-a-bloom-filter/
on “Bloom Filters for the Perplexed”Submitted Granular Audio Synthesis as a story · 153 points
HN discussionAre you familiar with automatic differentiation? https://blog.demofox.org/2014/12/30/dual-numbers-automatic-d... note that you get f(x) and f'(x) for some x without getting the derived function.
Comment linking /2014/12/30/dual-numbers-automatic-differentiation/
on “Why Bayesian Stats Needs Monte-Carlo Methods”Submitted Synthesizing a Plucked String Sound with the Karplus-Strong Algorithm as a story · 149 points
HN discussionAD can be done on paper. Analytical calculus derivatives get exponentially longer with the length of the derived expression. https://blog.demofox.org/2014/12/30/dual-numbers-automatic-d...
Comment linking /2014/12/30/dual-numbers-automatic-differentiation/
on “Differentiation for Hackers”Submitted Demystifying Floating Point Precision as a story · 147 points
HN discussionAD is NOT a numerical method, it's very precise. You can in fact do it on paper as well. https://blog.demofox.org/2014/12/30/dual-numbers-automatic-d... Analytical derivatives grow exponentially longer with the length of the expression. AD doesn't have this problem.
Comment linking /2014/12/30/dual-numbers-automatic-differentiation/
on “Differentiation for Hackers”Submitted Casual Shadertoy Path Tracing 1: Basic Camera, Diffuse, Emissive as a story · 139 points
HN discussionOne reason to use Blue noise in graphics / games / images is anytime you need a random number per pixel for, say, some Monte Carlo process, that will have a visible effect on the image and result in visible noise in the output. Using blue noise, the output will be visibly less “noisy” looking than when using white noise, due to blue noise having no low frequencies. Blue noise is best for situations where you only ha…
Comment linking /2020/05/16/using-blue-noise-for-raytraced-soft-shadows/
on “Why can’t you design noise in frequency space?”Submitted When random numbers are too random: Low discrepancy sequences (2017) as a story · 132 points
HN discussionNewbie here trying to follow. The prior post I link below suggests that what’s going on here is we are trying to find good points to sample an image. A challenge here is that the algorithms to generate the blue noise distributed sample points are slow. This motivates using an FT signal constructed by hand and then inverting this somehow to get sample points more quickly. But… he’s finding that the result doesn’t pla…
Comment linking /2017/10/20/generating-blue-noise-sample-points-with-mitchells-best-candidate-algorithm/
on “Why can’t you design noise in frequency space?”Submitted Dissecting "Tiny Clouds" shadertoy (2017) as a story · 122 points
HN discussionCurious to see whether more recent dithering approaches would produce better results. They don't even have to be more resource hungry than the classic Bayer or Floyd-Steinberg dithers! Interleaved Gradient Noise[0][1][2] comes to mind as an alternative to Bayer, and it can even be approximated quite well with just 8-bit operations! Basically, use the following function to determine your threshold based on pixel posi…
Comment linking /2022/01/01/interleaved-gradient-noise-a-different-kind-of-low-discrepancy-sequence/
on “Modos Paper Monitor Pre-Launch on Crowd Supply”Submitted Calculating the Distance Between Points in Wrap Around (Toroidal) Space as a story · 106 points
HN discussionThis talks about that more deeply and is by the same author (me) :) https://blog.demofox.org/2020/07/26/irrational-numbers/
Comment linking /2020/07/26/irrational-numbers/
on “When random numbers are too random: Low discrepancy sequences (2017)”Submitted Compressing Networked State Data as a story · 96 points
HN discussionActually you can make use of non-randomness in Monte Carlo simulations to get better results. There is various names for this, but the one I like best is "low discrepancy series". Have a look at [1] or [2] for a quick intro. These are sometimes also called quasi-random (or sub-random), but I find that a bit too close to pseudo-random. [1] https://en.wikipedia.org/wiki/Low-discrepancy_sequence [2] https://blog.demofo…
Comment linking /2017/05/29/when-random-numbers-are-too-random-low-discrepancy-sequences/
on “Billions of Random Numbers in a Blink of an Eye”Submitted The Double Headed Stack Allocator as a story · 95 points
HN discussionAD relies on dual numbers. Dual numbers are more suited for doing calculus. Structurally, dual numbers are numbers of the form a + b * e (where e is epsilon s.t. e^2 = 0 but e != 0. Think of it as the imaginary constant but instead of i^2 = -1, you have e^2=0). For example, multiplication of two dual numbers (a + b * e)(c + d * e) = (ac + ad * e + bc * e +bd * e^2). Since e^2 = 0, you end up with (ac + (ad + bc) * e…
Comment linking /2014/12/30/dual-numbers-automatic-differentiation/
on “Automatic Differentiation in Machine Learning: A Survey (2018) [pdf]”Submitted Markov Chain Text Generation as a story · 95 points
HN discussionBTW this older article of mine is extended with a new one that shows how to handle multiple variables (: http://blog.demofox.org/2017/02/20/multivariable-dual-number...
Comment linking /2017/02/20/multivariable-dual-numbers-automatic-differentiation/
on “Dual Numbers and Automatic Differentiation (2014)”Submitted Taking a Stroll Between the Pixels as a story · 95 points
HN discussionpart 1: https://blog.demofox.org/2020/05/25/casual-shadertoy-path-tr... You started part 1 with: > When you see a photorealistic image that someone says is “ray traced” what they likely mean is that it is “path traced” ... well, you just became my new hero. Thank you for saying what is my pet peeve ever since nVidia started using the term ray tracing for some stupid reason that I will never understand.
Comment linking /2020/05/25/casual-shadertoy-path-tracing-1-basic-camera-diffuse-emissive/
on “Casual Shadertoy Path Tracing 2: Image Improvement and Glossy Reflections”Submitted What I wish I knew about ESPP and RSUs sooner as a story · 88 points
HN discussionI'm not sure where they're getting that "lenses in pathtracers are ignored". They most certainly are not. How would physically based path tracing even work if they were? e.g. https://blog.demofox.org/2018/07/04/pathtraced-depth-of-fiel...
Comment linking /2018/07/04/pathtraced-depth-of-field-bokeh/
on “Lentil – Lenses for pathtracers”Submitted O(1) Data Lookups with Minimal Perfect Hashing as a story · 83 points
HN discussion
