├── .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: -------------------------------------------------------------------------------- 1 | github: [mxgmn] 2 | -------------------------------------------------------------------------------- /Apartemazements.md: -------------------------------------------------------------------------------- 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) 5 | 6 | Generation process: [https://youtu.be/PWyQ8Xy_lic](https://youtu.be/PWyQ8Xy_lic) 7 | 8 | Collection of generated results: [https://youtu.be/27Ye1JpcLO4](https://youtu.be/27Ye1JpcLO4) 9 | 10 | Twitter post: [twitter.com/exutumno/status/885128566173728768](https://twitter.com/exutumno/status/885128566173728768) 11 | 12 |

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16 | -------------------------------------------------------------------------------- /CarmaTower.md: -------------------------------------------------------------------------------- 1 | # CarmaTower 2 | A proceduralization of a [voxel scene](https://twitter.com/Sir_carma/status/851883489628704768) by Antoine Lendrevie. 3 | 4 | MarkovJunior model: [CarmaTower.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/CarmaTower.xml) 5 | 6 | Video: [https://youtu.be/JkbVpskDs6s](https://youtu.be/JkbVpskDs6s) 7 | 8 |

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55 | -------------------------------------------------------------------------------- /Escheresque.md: -------------------------------------------------------------------------------- 1 | # Escheresque 2 | Generating stairy scenes with full 3d local symmetry. 3 | 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). 5 | 6 | Twitter thread: [twitter.com/ExUtumno/status/895683455299723265](https://twitter.com/ExUtumno/status/895683455299723265) 7 | 8 |

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14 | -------------------------------------------------------------------------------- /ModernHouse.md: -------------------------------------------------------------------------------- 1 | # Generator of modern houses 2 | MarkovJunior model: [ModernHouse.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/ModernHouse.xml) 3 | 4 | Twitter thread: [twitter.com/ExUtumno/status/1141354217774428160](https://twitter.com/ExUtumno/status/1141354217774428160) 5 | 6 | Generation process: [https://www.youtube.com/watch?v=DTdIYa5k2us](https://www.youtube.com/watch?v=DTdIYa5k2us) 7 | 8 | Collection of generated results: [https://youtu.be/pjK8HfZb7LA](https://youtu.be/pjK8HfZb7LA) 9 | 10 |

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54 | -------------------------------------------------------------------------------- /PillarsOfEternity.md: -------------------------------------------------------------------------------- 1 | # PillarsOfEternity 2 | MarkovJunior model: [PillarsOfEternity.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/PillarsOfEternity.xml) 3 | 4 |

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7 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 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 | -------------------------------------------------------------------------------- /RandomSurface.md: -------------------------------------------------------------------------------- 1 | # Random surfaces 2 | MarkovJunior model: [Surface.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/Surface.xml) 3 | 4 | Twitter thread: [twitter.com/ExUtumno/status/900394891922071554](https://twitter.com/ExUtumno/status/900394891922071554) 5 | 6 |

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9 | -------------------------------------------------------------------------------- /SeaVilla.md: -------------------------------------------------------------------------------- 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. 3 | 4 | MarkovJunior model: [SeaVilla.xml](https://github.com/mxgmn/MarkovJunior/blob/master/models/SeaVilla.xml) 5 | 6 | Twitter thread: [twitter.com/ExUtumno/status/971031987304763393](https://twitter.com/ExUtumno/status/971031987304763393) 7 | 8 | Video: [https://youtu.be/L13XOHAV7jg](https://youtu.be/L13XOHAV7jg) 9 | 10 |

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60 | -------------------------------------------------------------------------------- /arttopc.md: -------------------------------------------------------------------------------- 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 | 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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 | --------------------------------------------------------------------------------