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The functional equation ξ(s) = ξ(1-s) identifies σ with 1-σ. Topologically, this turns the critical strip into a torus. The critical line σ = ½ is the throat. Now treat ξ(s) as a stream function. Its gradient is a velocity field. The flow is automatically: • Incompressible (ξ is holomorphic → Cauchy-Riemann → ∇·v = 0) • Symmetric (functional equation → v(σ) = v(1-σ)) THE CONNECTION Zeta Function Fluid Dynamics ───────────── ────────────── ξ(s) Stream function |ξ|² Pressure Zeros of ξ Pressure minima (p = 0) σ = ½ Torus throat THE THEOREM For symmetric incompressible flow on a torus, pressure…
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2015 · lewis500.github.io
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OP here: I created this visualization tool as the byproduct of a supply chain class I taught at Columbia. The pedagogical exercise grew into a full blown visualization and paper about global oil trade. The model: The mechanics are the same as the financial network Eisenberg-Noe: Instead of banks, every country consumes oil interconnected via bilateral trading. Shocks propagate throughout the network, depleting oil reserves when bottleneck nodes (such as the Strait of Hormuz) are blocked. Insights: The interesting part is the mechanics of how the crisis unfolds: for example, France receives 0…
Jul 2026 · globaloilnetwork.staffinganalytics.io
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Trying to do gradient descent using automatic differentiation over branchy programs? Or to combine them with neural networks for end-to-end training? Then this might be interesting to you. We develped DiscoGrad, a tool for automatic differentiation through C++ programs involving input-dependent control flow (e.g., "if (f(x) < c) { ... }", differentiating wrt. x) and randomness. Our initial motivation was to enable the use of gradient descent with simulations, which often rely heavily on such discrete branching. The latter makes plain autodiff mostly useless, since it can only account for the…
2024 · github.com
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2019 · github.com
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Hello HN, It has been a while since I contributed to the web, so I decided to get back in shape and publish "something". This app is a POC of "what if diagrams were more dynamic". I'm a software engineer by trade, and with conventional tools, I often times struggle to explain flows of data in complex software systems. I got inspired by video games like The Incredible Machine and Factorio, as in some ways, software systems tend to become Rube Goldberg-esque machines ;) As a side quest, I also wanted to craft diagrams faster than text-based tools (ex: mermaid), as I am always forgetting their…
2024 · github.com
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2019 · analytech-solutions.com
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We ported pbrt-v4 to Julia and built it into a Makie backend. Any Makie plot can now be rendered with physically-based path tracing. Julia compiles user-defined physics directly into GPU kernels, so anyone can extend the ray tracer with new materials and media - a black hole with gravitational lensing is ~200 lines of Julia. Runs on AMD, NVIDIA, and CPU via KernelAbstractions.jl, with Metal coming soon. Demo scenes: github.com/SimonDanisch/RayDemo
Feb 2026 · makie.org
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(space = reset) Fluid mechanics is an extremely interesting topic and I have been creative coding for a couple of months now. Therefore I started working on flow fields in processing. It had so much fun playing around with the different parameters in this project, I decided to rewrite in p5.js an added a control panel. You can change most of the parameters (within some constraints I thought to be reasonable), randomize the values and export and import settings. Hopefully some coders here get inspired and also join the great creative coding community.
2024 · synapse.nugatio.com
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Features include: - Several preset periodic orbits: the classic Figure-8, plus newly discovered 3D solutions from Li and Liao's recent database of 10,000+ orbits (https://arxiv.org/html/2508.08568v1) - Full 3D camera controls (rotate/pan/zoom) with body-following mode - Force and velocity vector visualization - Timeline scrubbing to explore the full orbital period The 3D presets are particularly interesting. Try "O₂(1.2)" or "Piano O₆(0.6)" from the Load Presets menu to see configurations where bodies weave in and out of the orbital plane. Most browser…
Nov 2025 · trisolarchaos.com
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This little project came about because I kept running into the same problem: cleanly differentiating sensor data before doing analysis. There are a ton of ways to solve this problem, I've always personally been a fan of using kalman filters for the job as its easy to get the double whammy of resampling/upsampling to a fixed consistent rate and also smoothing/outlier rejection. I wrote a little numpy only bayesian filtering/smoothing library recently (https://github.com/hugohadfield/bayesfilter/) so this felt like a fun and very useful first thing to…
2024 · github.com
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OP here. This is a geometric decoding of Chopin's Prelude No. 4. I built a 3D music midi visualizer ( https://github.com/jimishol/cholidean-harmony-structure ) and realized that standard music theory couldn't explain the shapes I was seeing. So, I developed the Umbilic-Surface Grammar to map the topology of the harmony. This document demonstrates that the prelude's tension isn't random, but a rigorous conflict between 'Gravity' (Station Shifts) and 'Will' (Pivots). I am looking for feedback on the logic—specifically from anyone with a background in topology or music…
Feb 2026 · github.com
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Line9 is a new rendering engine for Mermaid flowchart diagrams that aims to remove the need for manual adjustment of layout. Mermaid is a popular text-based language for describing multiple types of diagrams. Several Mermaid rendering engines already exist. Most, like the original mermaid.js, use Dagre or ELK graph drawing libraries to automatically lay out their diagrams. I’ve used Mermaid for the past four years but often recreated my flowcharts in a diagram editor so that I could modify the layout to something that better suited my needs. Use Line9 when you want an automatic flowchart…
Aug 2026 · line9.ai
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Zero-Knowledge Proofs (ZKPs) let an untrusted proved show that computation was executed correctly without revealing the inputs to the verifier. However to prove anything, the computation first has to be expressed as a circuit: a system of polynomial equations (constraints) over a finite field. Circuits are the assembly language of zk and every constraint costs prover (and sometimes verifier) time, so production circuits are aggressively hand-optimized. Over the last months, we have been experimenting with writing formal specifications instead and letting LLMs produce the circuits: as long as…
Jul 2026 · zk.golf
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2022 · github.com
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I've always been dissatisfied that simple Mandelbrot explorers proport themselves as a Fractal Graphing Calculator. In summer break between semesters, I started making a real graphing calculator, parsing LaTeX to WebGL to let you graph most any combination of z and c. Fun ones to try include - sin(z^2+c) - c^z - z^{1.7}+c Also supports animation, just enter any other letter and turn it into a variable. Supports Mandelbrot or Julia Set style calculation. Use with a graphics card or integrated graphics
2025 · juliascope.com
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2021 · colab.research.google.com
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2023 · bruijn.marvinborner.de
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I analyzed two orderings of the 64 I Ching hexagrams and found the permutation cycle decomposition between them is [52, 10, 2] with zero fixed points. Nobody has done this kind of analysis before and this cycle type has not been reported in the literature. You can verify it yourself.
Mar 2026 · gzw1987-bit.github.io
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I'm excited to introduce a new beta version of LIPS Scheme. The most important features of this
20d ago · lips.js.org
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A functional programming and concurrency library for Python: algebraic abstractions (Semigroups, Monoids, Functors, Applicatives, Monads), immutable data types, and message-passing concurrency, all designed as composable, type-safe values. - kamalfarahani/katharos
Aug 2026 · github.com
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