davidar

"""
Polykite Tiling Explorer

Author: OpenAI GPT-4

Description:
This script explores the tiling properties of polykites, specifically those with 8 components.
It generates all possible polykites with 8 components, canonicalizes them to avoid duplicate
analysis, and then computes their isohedral numbers to identify interesting candidates for further
mathematical exploration.

davidar

davidar

#!/bin/bash
# http://superuser.com/a/1068709/55113
for file in ~/.local/share/applications/*.desktop; do
    CLASS="`grep '^StartupWMClass=' "$file" | cut -d= -f2`"
    if [ -n "$CLASS" ] && ! grep -q xdotool "$file"; then
        EXEC="`grep '^Exec=' "$file"`"
        EXEC="$EXEC \\&\\& xdotool search --sync --classname $CLASS set_window --class $CLASS"
        sed -i~ "s!^Exec=.*!$EXEC!" "$file"
    fi
done

davidar

// 2022 David A Roberts <https://davidar.io/>

// https://www.jcgt.org/published/0009/03/02/
// https://www.pcg-random.org/
fn pcg(seed: ptr<function, uint>) -> float {
    *seed = *seed * 747796405u + 2891336453u;
    let word = ((*seed >> ((*seed >> 28u) + 4u)) ^ *seed) * 277803737u;
    return float((word >> 22u) ^ word) / float(0xffffffffu);
}

davidar

// Based on the path tracing tutorial series by demofox:
// https://blog.demofox.org/2020/05/25/casual-shadertoy-path-tracing-1-basic-camera-diffuse-emissive/

let MINIMUM_RAY_HIT_TIME = .1;
let FAR_PLANE = 1e4;
let FOV_DEGREES = 90.;
let NUM_BOUNCES = 8;
let RAY_POS_NORMAL_NUDGE = .01;
let NUM_RENDERS_PER_FRAME = 100;
let EXPOSURE = .5;

davidar

// 2022 David A Roberts <https://davidar.io/>

// https://www.shadertoy.com/view/4djSRW
fn hash44(p: float4) -> float4 {
    var p4 = fract(p * float4(.1031, .1030, .0973, .1099));
    p4 = p4 + dot(p4, p4.wzxy+33.33);
    return fract((p4.xxyz+p4.yzzw)*p4.zywx);
}

let dt = 1.;

davidar

fn isfinite(x: f32) -> bool {
    return clamp(x, -3.4e38, 3.4e38) == x;
}

fn hash12(p: float2) -> float {
    var p3  = fract(float3(p.xyx) * .1031);
    p3 += dot(p3, p3.yzx + 33.33);
    return fract((p3.x + p3.y) * p3.z);
}

davidar

/* Partial port of PBRT v3 <https://github.com/mmp/pbrt-v3> to WGSL.

BSD 2-Clause License

Copyright (c) 1998-2015, Matt Pharr, Greg Humphreys, and Wenzel Jakob
Copyright (c) 2022, David A Roberts <https://davidar.io/>

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

davidar

fn pcg_random(seed: ptr<function, uint>) -> float {
    *seed = *seed * 747796405u + 2891336453u;
    let word = ((*seed >> ((*seed >> 28u) + 4u)) ^ *seed) * 277803737u;
    return float((word >> 22u) ^ word) / float(0xffffffffu);
}

// weighted coin flip (bernoulli)
fn flip(state: ptr<function, uint>, p: float) -> bool {
    return pcg_random(state) <= p;
}

davidar

MIT License

Copyright (c) 2013 Inigo Quilez <https://iquilezles.org/>
Copyright (c) 2013 Nikita Miropolskiy
Copyright (c) 2022 David A Roberts <https://davidar.io/>

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell