├── .github
└── FUNDING.yml
├── Apartemazements.md
├── CarmaTower.md
├── Escheresque.md
├── ModernHouse.md
├── PillarsOfEternity.md
├── README.md
├── RandomSurface.md
├── SeaVilla.md
├── arttopc.md
├── exams
├── analysis.pdf
├── arithmetics++.pdf
├── arithmetics+.pdf
├── arithmetics.pdf
├── basic+++.pdf
├── basic++.pdf
├── basic+.pdf
├── basic-alt.pdf
├── basic-theory.pdf
├── basic.pdf
├── combinatorics-.pdf
├── combinatorics.pdf
├── complex.pdf
├── coordinates.pdf
├── derivative+.pdf
├── derivative.pdf
├── dot.pdf
├── ehp.pdf
├── equivalence.pdf
├── graph++.pdf
├── graph+.pdf
├── graph-parametric.pdf
├── graph-polar.pdf
├── graph.pdf
├── induction.pdf
├── logarithm.pdf
├── numbers+.pdf
├── numbers.pdf
├── olymp-graphs.pdf
├── olymp-invariant.pdf
├── olymp-pigeon.pdf
├── parameters.pdf
├── plane+.pdf
├── plane-area.pdf
├── plane-circles.pdf
├── plane-constructions.pdf
├── plane-gmt.pdf
├── plane-right.pdf
├── plane-similarity.pdf
├── plane-triangle.pdf
├── polynomials+.pdf
├── polynomials.pdf
├── sets-.pdf
├── sets.pdf
├── stereo.pdf
└── trigonometry.pdf
├── godel.pdf
├── images
├── Apartemazements
│ ├── big.png
│ ├── borg.png
│ ├── large.png
│ └── small.png
├── CarmaTower
│ ├── 0.png
│ ├── 1.png
│ ├── 10.png
│ ├── 11.png
│ ├── 12.png
│ ├── 13.png
│ ├── 14.png
│ ├── 15.png
│ ├── 16.png
│ ├── 17.png
│ ├── 18.png
│ ├── 19.png
│ ├── 2.png
│ ├── 20.png
│ ├── 21.png
│ ├── 22.png
│ ├── 23.png
│ ├── 24.png
│ ├── 25.png
│ ├── 26.png
│ ├── 27.png
│ ├── 28.png
│ ├── 29.png
│ ├── 3.png
│ ├── 30.png
│ ├── 31.png
│ ├── 32.png
│ ├── 33.png
│ ├── 34.png
│ ├── 35.png
│ ├── 36.png
│ ├── 37.png
│ ├── 38.png
│ ├── 39.png
│ ├── 4.png
│ ├── 40.png
│ ├── 41.png
│ ├── 42.png
│ ├── 43.png
│ ├── 44.png
│ ├── 5.png
│ ├── 6.png
│ ├── 7.png
│ ├── 8.png
│ └── 9.png
├── Escheresque
│ ├── 0.png
│ ├── 1.png
│ ├── 2.png
│ ├── 3.png
│ └── partially-observed.png
├── ModernHouse
│ ├── 01.png
│ ├── 02.png
│ ├── 03.png
│ ├── 04.png
│ ├── 05.png
│ ├── 06.png
│ ├── 07.png
│ ├── 08.png
│ ├── 09.png
│ ├── 10.png
│ ├── 11.png
│ ├── 12.png
│ ├── 13.png
│ ├── 14.png
│ ├── 15.png
│ ├── 16.png
│ ├── 17.png
│ ├── 18.png
│ ├── 19.png
│ ├── 20.png
│ ├── 21.png
│ ├── 22.png
│ ├── 23.png
│ ├── 24.png
│ ├── 25.png
│ ├── 26.png
│ ├── 27.png
│ ├── 28.png
│ ├── 29.png
│ ├── 30.png
│ ├── 31.png
│ ├── 32.png
│ ├── 33.png
│ ├── 34.png
│ ├── 35.png
│ ├── 36.png
│ ├── 37.png
│ ├── 38.png
│ ├── 39.png
│ └── other
│ │ ├── 4.png
│ │ ├── 6a.png
│ │ ├── 6b.png
│ │ └── 7.png
├── PillarsOfEternity
│ ├── 0.png
│ ├── 1.png
│ └── 2.png
├── RandomSurface
│ ├── 10.png
│ ├── mc.png
│ └── tiles.png
├── SeaVilla
│ ├── 1.png
│ ├── 10.png
│ ├── 11.png
│ ├── 12.png
│ ├── 13.png
│ ├── 14.png
│ ├── 15.png
│ ├── 16.png
│ ├── 17.png
│ ├── 18.png
│ ├── 19.png
│ ├── 2.png
│ ├── 20.png
│ ├── 21.png
│ ├── 22.png
│ ├── 23.png
│ ├── 24.png
│ ├── 25.png
│ ├── 26.png
│ ├── 27.png
│ ├── 28.png
│ ├── 29.png
│ ├── 3.png
│ ├── 30.png
│ ├── 31.png
│ ├── 32.png
│ ├── 33.png
│ ├── 34.png
│ ├── 4.png
│ ├── 5.png
│ ├── 6.png
│ ├── 7.png
│ ├── 8.png
│ ├── 9.png
│ └── other
│ │ ├── 13-0.png
│ │ ├── 13-1.png
│ │ ├── 13-2.png
│ │ ├── 13-3.png
│ │ ├── 6.png
│ │ ├── 7.png
│ │ ├── 8.png
│ │ ├── 9.png
│ │ ├── rect-13.png
│ │ ├── rect-6.png
│ │ ├── rect-7.png
│ │ ├── rect-9.png
│ │ └── top.png
├── lmsh
│ ├── coordinates-50.png
│ ├── derivative.pdf
│ ├── groups.png
│ ├── hyperbolic-day.png
│ ├── hyperbolic-night.png
│ ├── minmax.png
│ ├── probability.pdf
│ ├── processes.png
│ ├── projective-geometry.png
│ └── topology.png
└── squircles
│ ├── arms.gif
│ ├── fg.gif
│ ├── lame.gif
│ ├── lerp.gif
│ └── levelsets.gif
├── qft
├── problems-0.pdf
├── problems-1.pdf
├── problems-2.pdf
├── problems-3.pdf
├── problems-4.pdf
├── problems-5.pdf
└── problems-c.pdf
└── squircles.md
/.github/FUNDING.yml:
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1 | github: [mxgmn]
2 |
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/Apartemazements.md:
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1 | # Apartemazements
2 | Procedural apartemazements, for a modern minotaur to live in.
3 |
4 | MarkovJunior model: [Apartemazements.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/Apartemazements.xml)
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6 | Generation process: [https://youtu.be/PWyQ8Xy_lic](https://youtu.be/PWyQ8Xy_lic)
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8 | Collection of generated results: [https://youtu.be/27Ye1JpcLO4](https://youtu.be/27Ye1JpcLO4)
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10 | Twitter post: [twitter.com/exutumno/status/885128566173728768](https://twitter.com/exutumno/status/885128566173728768)
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/CarmaTower.md:
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1 | # CarmaTower
2 | A proceduralization of a [voxel scene](https://twitter.com/Sir_carma/status/851883489628704768) by Antoine Lendrevie.
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4 | MarkovJunior model: [CarmaTower.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/CarmaTower.xml)
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6 | Video: [https://youtu.be/JkbVpskDs6s](https://youtu.be/JkbVpskDs6s)
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/Escheresque.md:
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1 | # Escheresque
2 | Generating stairy scenes with full 3d local symmetry.
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4 | MarkovJunior models: [Escher.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/Escher.xml), [EscherSurface.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/EscherSurface.xml), [PeriodicEscher.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/PeriodicEscher.xml), [OrientedEscher.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/OrientedEscher.xml).
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6 | Twitter thread: [twitter.com/ExUtumno/status/895683455299723265](https://twitter.com/ExUtumno/status/895683455299723265)
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/ModernHouse.md:
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1 | # Generator of modern houses
2 | MarkovJunior model: [ModernHouse.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/ModernHouse.xml)
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4 | Twitter thread: [twitter.com/ExUtumno/status/1141354217774428160](https://twitter.com/ExUtumno/status/1141354217774428160)
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6 | Generation process: [https://www.youtube.com/watch?v=DTdIYa5k2us](https://www.youtube.com/watch?v=DTdIYa5k2us)
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8 | Collection of generated results: [https://youtu.be/pjK8HfZb7LA](https://youtu.be/pjK8HfZb7LA)
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/PillarsOfEternity.md:
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1 | # PillarsOfEternity
2 | MarkovJunior model: [PillarsOfEternity.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/PillarsOfEternity.xml)
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/README.md:
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1 | Research:
2 | * [Applying random transformations to other people's code](arttopc.md)
3 |
4 | Explanations:
5 | * [Squircles](squircles.md)
6 |
7 | Procedural voxel art:
8 | * [ModernHouse](ModernHouse.md)
9 | * [SeaVilla](SeaVilla.md)
10 | * [Apartemazements](Apartemazements.md)
11 | * [CarmaTower](CarmaTower.md)
12 | * [Escheresque](Escheresque.md)
13 | * [PillarsOfEternity](PillarsOfEternity.md)
14 | * [RandomSurface](RandomSurface.md)
15 |
16 | In Russian:
17 | * [Introduction to Quantum Field Theory problem sets](qft/) at [HSE Faculty of Mathematics](https://math.hse.ru/en/)
18 | * [Introduction to Mathematical Logic: Theory of Computation and the Incompleteness Theorems](godel.pdf)
19 | * [School problem sets](exams/)
20 |
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/RandomSurface.md:
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1 | # Random surfaces
2 | MarkovJunior model: [Surface.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/Surface.xml)
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4 | Twitter thread: [twitter.com/ExUtumno/status/900394891922071554](https://twitter.com/ExUtumno/status/900394891922071554)
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/SeaVilla.md:
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1 | # Generator of Sea Villa puzzles
2 | The player arrives by boat. Goal: grab the shiny blue cube and get back. Wooden bridges collapse after one pass, consoles open gates wired to them. Guaranteed to be solvable and without shortcuts.
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4 | MarkovJunior model: [SeaVilla.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/SeaVilla.xml)
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6 | Twitter thread: [twitter.com/ExUtumno/status/971031987304763393](https://twitter.com/ExUtumno/status/971031987304763393)
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/arttopc.md:
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1 | # Applying random transformations to other people's code
2 |
3 | Experiments in program generation and synthesis.
4 |
5 | Season 1 | videos | original | comment
6 | --- | --- | --- | ---
7 | [Episode 1](https://twitter.com/ExUtumno/status/1276530276026458113) | [mp4](https://i.imgur.com/Sy9FqHl.mp4), [mp4](https://i.imgur.com/2ss3ULN.mp4) | [2DArray](https://twitter.com/2DArray/status/1183789478185439233) | mapping from plane to colors
8 | [Episode 2](https://twitter.com/ExUtumno/status/1276567879664709633) | [mp4](https://drive.google.com/file/d/1Ck3DSpnacESk8W3cLl5h49KMultSCxFj/view) | [bjornkri](https://twitter.com/bjornkri/status/1239193587046367232) | surface made of circles
9 | [Episode 3](https://twitter.com/ExUtumno/status/1278713838586789889) | [mp4](https://i.imgur.com/MwNlFHu.mp4) | [anastasiaopara](https://twitter.com/anastasiaopara/status/1256198343740592128) | integer and fractional parts, squircles
10 | [Episode 4](https://twitter.com/ExUtumno/status/1281228686264500228) | [mp4](https://i.imgur.com/1qzsljt.mp4) | [voxeledphoton](https://twitter.com/voxeledphoton/status/1067487792765247489) | generator of curves
11 | [Episode 5](https://twitter.com/ExUtumno/status/1286315543981633536) | [mp4](https://i.imgur.com/ml02NR9.mp4) | [lucatron_](https://twitter.com/lucatron_/status/1203444384357683200) | reading grid values
12 | [Episode 6](https://twitter.com/ExUtumno/status/1291386335232765963) | [mp4](https://i.imgur.com/KgsJRnm.mp4) | [FreyaHolmer](https://twitter.com/FreyaHolmer/status/1236079824575369219) | curves from a surface, first interpolation
13 | Episode 7 | [mp4](https://i.imgur.com/wB5UTXX.mp4) | [guerragames](https://twitter.com/guerragames/status/1097236590915710988) | local transformations
14 | Episode 8 | mp4 | ??? | integration, Euler spiral
15 | Episode 9 | mp4 | ??? | ???
16 | Episode 10 | mp4 | ??? | 2d palette
17 |
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1 | # Squircles
2 | While [experimenting](arttopc.md) with [program synthesis](https://en.wikipedia.org/wiki/Program_synthesis), I [found](https://twitter.com/ExUtumno/status/1278713838586789889) an interesting mathematical curiosity, [squircles](https://en.wikipedia.org/wiki/Squircle). Squircle is a curve that interpolates between a square and a circle.
3 |
4 | The most obvious way to get a squircle is just to linearly interpolate between a square and a circle in polar coordinates. However, the resulting intermediate curves are not smooth!
5 | 
6 |
7 | The most famous smooth squircle is probably the [Lamé curve](https://en.wikipedia.org/wiki/Superellipse), also known as superellipse. This squircle is actually an exact circle, but with respect to the non-Euclidean [p-norm](https://en.wikipedia.org/wiki/Lp_space) (it's Euclidean for `p=2`)!
8 | 
9 |
10 | In a [1992 paper](https://www.tandfonline.com/doi/abs/10.1080/0020739920230607), Fernández-Guasti describes an algebraic squircle. Algebraic means that it's described by an equation consisting only of variables, numbers, addition and multiplication.
11 | 
12 |
13 | Full solutions of the Fernández-Guasti's equation actually contain 4 unbounded arms in addition to the squircular figure in the middle:
14 | 
15 |
16 | You could have discovered the Fernández-Guasti squircles by looking at the function `F(x,y)=1-x^2-y^2+x^2y^2`. Its level sets are expanding squircles: the unit square is the `0`-set, and near the center `x^2y^2` is too small, so the level sets tend to be circles in the center.
17 | 
18 |
19 | Additional material:
20 | 1. [Original paper](https://www.tandfonline.com/doi/abs/10.1080/0020739920230607) by Fernández-Guasti. Paywalled, accessible via Sci-Hub.
21 | 2. In [Squircular Calculations](https://arxiv.org/vc/arxiv/papers/1604/1604.02174v1.pdf) Chamberlain Fong generalizes Fernández-Guasti squircle to 3d.
22 |
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