Attempting to improve my Rubik's Cube solver with viewer suggestions such as: CFOP, domino reduction, and pruning tables. Links: Support my work (and get early access to new projects): https://www.patreon.com/SebastianLague Source code: https://github.com/SebLague/Rubiks-Cube Previous Rubik's cube video: https://youtu.be/fy0HRViXZnE Resources and credits: https://www.kociemba.org/cube.htm https://en.wikipedia.org/wiki/Optimal_solutions_for_the_Rubik%27s_Cube Music: https://raw.githubusercontent.com/SebLague/Misc-Project-Info/refs/heads/main/Coding-Adventures/Rubiks2.txt Chapters: 00:00 Intro 00:23 Cross 02:06 F2L 05:40 OLL 08:00 PLL 09:57 Domino Reduction 14:41 Iterative Deepening 16:10 IDA* 18:26 Prune Tables 22:52 Multi-Search 25:11 Final Results 26:11 Raytracing?

My attempt at solving the 3x3 Rubik's cube (by programming the computer to do it for me). Note: in the evaluation function at 22:32 I mention that it falls back to the 'Greedy' evaluator shown previously. However, I forgot that I had made a small change to that function, which is to give a bonus to correctly oriented corners. Sorry for the oversight! Links: Support my work (and get early access to new projects): https://www.patreon.com/SebastianLague Source code: https://github.com/SebLague/Rubiks-Cube Follow-up video: https://youtu.be/Eysf6-E3ino?is=Fu6gW1WFUXyDTQoa Resources and credits: https://en.wikipedia.org/wiki/Optimal_solutions_for_the_Rubik%27s_Cube https://raw.githubusercontent.com/SebLague/Misc-Project-Info/refs/heads/main/Coding-Adventures/RubiksCube.txt Chapters: 00:00 Creating the Cube 02:00 Rotation Time! 04:39 Binary State 08:15 Making Moves 12:47 Search and Optimization 15:34 The Greedy Solver 17:53 The Sandwich Solver 20:21 The Oriented Solver 23:39 Final Thoughts

Let's try add sine waves together and see what sort of sounds we can create! Support my work (and get early access to new videos and source code) on Patreon: https://www.patreon.com/SebastianLague Project files: https://github.com/SebLague/Audio-Experiments Resources and credits: https://www.soundonsound.com/series/synth-secrets-sound-sound https://theremin.music.uiowa.edu/MISpiano.html (currently inaccessible?) https://www.youtube.com/watch?v=atvtBE6t48M https://raw.githubusercontent.com/SebLague/Misc-Project-Info/refs/heads/main/Coding-Adventures/musicSynth.txt Chapters: 00:00 Intro 01:28 Synth Setup 02:32 Precision Issues 04:19 ADR Envelope 06:35 Curvy Envelopes 08:22 Multiple Notes! 09:32 Compressor 11:52 Twelve Equal Temperament 14:21 Scales and Piano Layout 15:46 MIDI 17:51 Harmonics 22:03 Some Tweaks 25:02 Atonal Test 26:07 Interpolation 27:16 Low Octaves 30:12 Simple Piano Synth 30:35 Sin Bug 31:35 Simple Marimba Synth 32:25 Sustain 33:42 Outro and Final Test

Let's have some fun messing about with sound and the Short-Time Fourier Transform! Support my work (and get early access to new videos and source code) on Patreon: https://www.patreon.com/SebastianLague Project files: https://github.com/SebLague/Audio-Experiments This is a follow-up to my previous audio-based episode, which you can watch over here: https://www.youtube.com/watch?v=iA6wRgwl7k0 Music credits: https://raw.githubusercontent.com/SebLague/Misc-Project-Info/refs/heads/main/Coding-Adventures/stft.txt Chapters: 00:00 Intro 02:17 The Short-Time Fourier Transform 04:47 Time and Frequency Resolution 08:14 Single Frequency Experiment 10:25 Creating a Spectrogram 11:48 Hann Window 14:43 Hop and Segment Size 15:57 Spectrogram to Sound 17:05 Painting Sound 20:04 Secret Messages 20:44 Outro

The white pixels in the original animation have been treated as solid cells (drawn in black), with a constant outwards force applied along the outline. Smoke is also gradually added in along the outline. Simulation explanation: https://www.youtube.com/watch?v=Q78wvrQ9xsU My other bad apple (using a particle-based fluid): https://www.youtube.com/watch?v=2Ni13dnAbSA Support my random experiments on Patreon: https://www.patreon.com/SebastianLague Credits: Music: https://www.youtube.com/watch?v=i41KoE0iMYU Animation by あにら (Anira). Specifically, I used this version: https://www.youtube.com/watch?v=FtutLA63Cp8 Subtitles: https://archive.org/details/bad-apple-resources

My attempt at coding a grid-based fluid simulation to try and achieve some smoky effects! Support my work (and get early access to new videos and source code) on Patreon: https://www.patreon.com/SebastianLague Source Code: https://github.com/SebLague/Smoke-Simulation Resources and References: Fluid notes: https://www.cs.ubc.ca/~rbridson/fluidsimulation/fluids_notes.pdf Ten-minute physics: https://www.youtube.com/watch?v=iKAVRgIrUOU My other fluid videos: https://youtube.com/playlist?list=PLFt_AvWsXl0dJrPelwdVSMVC_MDTYPJWn&si=Z5cOCDSI1aS4fe_C Sound wave simulation: https://www.youtube.com/watch?v=iA6wRgwl7k0 Music: https://raw.githubusercontent.com/SebLague/Misc-Project-Info/refs/heads/main/Coding-Adventures/Smoke Chapters 00:00 Intro 00:50 Navier-Stokes Equations 02:00 Divergence 05:09 Solving for Pressure 08:26 Gauss-Seidel Iteration 10:36 Solid Cells 12:26 Velocity Interpolation 15:15 Advection (with derivatives) 18:37 Semi-Lagrangian Advection 22:12 Testing 23:43 Successive Over-Relaxation 25:16 Visualizing Speed 26:32 Smoke Map 28:14 Parallel Pressure Solving 31:13 Vortex Shedding 35:48 A Few Little Experiments 37:55 Temperature 39:17 Final Smoke Experiments 40:38 Outro

It's been almost 7 years since I last took part in a game jam, so I felt it was high time to jam again! The goal was to make something in 4 days, inspired by the single word: LOOP. Support my work (and get early access to new videos and source code) on Patreon: https://www.patreon.com/SebastianLague Source code and game download: * GitHub: https://github.com/SebLague/Family-Time * Play: https://sebastian.itch.io/family-time Credits and other links: * Game assets: https://github.com/SebLague/Family-Time/blob/main/Assets/3rdParty.txt * Video music: https://github.com/SebLague/Misc-Project-Info/blob/main/Other%20Videos/FamilyTime.txt * All games: https://itch.io/jam/gmtk-2025/entries * Games shown at end: -- Planet Looper: https://itch.io/jam/gmtk-2025/rate/3763752 -- Cursed by Feedback: https://itch.io/jam/gmtk-2025/rate/3775683 -- CRANK IT: https://itch.io/jam/gmtk-2025/rate/3768606 -- Sir Loopsalot: https://itch.io/jam/gmtk-2025/rate/3771619 -- Time Prison: https://itch.io/jam/gmtk-2025/rate/3779083 -- GLORBIT Saves the Galaxy: https://itch.io/jam/gmtk-2025/rate/3778815 Chapters: 00:00 Day Zero 00:55 Day One 05:48 Day Two 09:52 Day Three 14:55 Day Four 20:38 Playthrough

Let's do some more ray-tracer coding and see if we can get it to render glass, and rainbows, and more! Support my work (and get early access to new videos and source code) on Patreon: https://www.patreon.com/SebastianLague Source code: https://github.com/SebLague/Ray-Tracing Credits: * Music: https://github.com/SebLague/Misc-Project-Info/blob/main/Coding-Adventures/GlassAndCaustics.txt * Frosted glass reference: https://youtu.be/fWAAOWTV1K0?si=KL-EnzSZ6mLVfuqn Chapters: 00:00 Intro 02:02 Glass 04:58 Glass Bugs 09:04 NaNs 11:51 Absorption 13:49 Frosted Glass 15:44 Glass Ball Test 21:14 Stack versus Stoch 22:55 Visualizing Caustics 25:42 Cardioid Caustic 27:04 Water Caustic 32:24 Rainbow 36:01 Spectral Experiment 40:46 Outro

Let's try to turn some dot products into a 3D world! Support my work (and get early access to new videos and source code) on Patreon or Nebula * Patreon: https://www.patreon.com/SebastianLague * Nebula: https://go.nebula.tv/sebastianlague Source code: * GitHub: https://github.com/SebLague/Software-Rasterizer Credits: * Music: https://raw.githubusercontent.com/SebLague/Misc-Project-Info/refs/heads/main/Coding-Adventures/Rasterizer.txt * Raylib: https://github.com/raysan5/raylib * C# bindings: https://github.com/raylib-cs/raylib-cs * Visualizations made (mostly) with Shapes: https://acegikmo.com/shapes/ Chapters: 00:00 Intro 00:32 The First Image 02:39 Triangle Maths 05:36 Testing the Triangles 07:30 Reading a 3D Model 09:13 Orthographic Projection 10:20 Single-Axis Rotation 12:37 Back-Face Culling 13:42 Another Axis of Rotation 15:34 Perspective and Field of View 19:22 Monkey! (and the Depth Buffer) 25:30 Real-Time Rendering 26:31 Camera and View Space 31:22 Depth Bug 33:03 Textures 35:00 Directional Lighting 38:52 Boy and Fox 40:35 Near-Plane Clipping 43:49 Procedural Terrain 45:18 Some Quick Optimizations 46:32 Odds and Ends 48:40 Final Demo

Let’s try building a whopping 256 bytes of random access memory (inside a digital logic simulation). This is part 5 of my journey to explore the basics of how computer’s work. If you’d like to watch the other episodes, you can find the full playlist here: https://youtube.com/playlist?list=PLFt_AvWsXl0dPhqVsKt1Ni_46ARyiCGSq&si=tYFx249Y6Nufctdb The simulation program is in a slightly rough and unstable state as I’m developing it as I go, but if you’d like to try it out, the latest version (and source code) is available over here: https://sebastian.itch.io/digital-logic-sim https://github.com/SebLague/Digital-Logic-Sim If you’d like to support me in creating more videos, consider becoming a patron of the channel: https://www.patreon.com/c/SebastianLague This series was largely inspired by the 8-bit breadboard computer series by @BenEater (so be sure to check that out if you haven’t already)! Image and music credits: https://raw.githubusercontent.com/SebLague/Misc-Project-Info/refs/heads/main/Digital-Logic-Sim/ram-credits.txt Chapters: 00:00 Intro and a New Simulation 01:50 A Grid of Latches 03:12 Decoder 04:42 1-Bit Memory Cell 06:42 Rambling about Dynamic and Static Memory 08:46 16 Bits of Memory 11:41 Surprise Inspection 12:16 256 Bits of Memory 14:28 Asynchronous RAM 18:02 A Brief Note Concerning Caches 19:00 Synchronous RAM 22:28 Equality Chip 23:28 The Final Test 24:37 A Trip Down Memory Lane

Until today, the Fluid Simulation has been confined to a tiny box. Let's set it free on a planet, with a little orbiting moon, and see what happens! Support my work (and get early access to new videos and source code) on Patreon or Nebula * Patreon: https://www.patreon.com/SebastianLague * Nebula: https://go.nebula.tv/sebastianlague Source Code: * GitHub https://github.com/SebLague/Fluid-Planet Check out my other fluid simulation videos: https://youtube.com/playlist?list=PLFt_AvWsXl0dJrPelwdVSMVC_MDTYPJWn&si=Z5cOCDSI1aS4fe_C Credits: * Music: https://raw.githubusercontent.com/SebLague/Misc-Project-Info/refs/heads/main/Coding-Adventures/FluidPlanet.txt Chapters: 00:00 Intro 00:25 Playing with Gravity 03:11 Adding Simple Collisions 04:21 Implementing Orbits 05:36 Visualizing Tidal Forces 07:46 Fluid Shell 08:50 Tide Watching 11:54 Implementing the Earth 17:25 Oceans on Earth 20:26 A Terraforming Experiment 23:48 3-Body System

We've succeeded in the past to make a bunch of little balls behave like a fluid, but can we now make them look like a fluid too? In this video we'll explore a few different techniques, and also attempt a simple simulation of foam and spray to liven things up! Support my work (and get early access to new videos and source code) on Patreon or Nebula * Patreon: https://www.patreon.com/SebastianLague * Nebula: https://go.nebula.tv/sebastianlague Source Code: * GitHub: https://github.com/SebLague/Fluid-Sim Check out my other fluid simulation videos: https://youtube.com/playlist?list=PLFt_AvWsXl0dJrPelwdVSMVC_MDTYPJWn&si=Z5cOCDSI1aS4fe_C Credits and References: * Screen Space Fluid Rendering: https://developer.download.nvidia.com/presentations/2010/gdc/Direct3D_Effects.pdf * Foam, Spray and Bubbles: https://cg.informatik.uni-freiburg.de/publications/2012_CGI_sprayFoamBubbles.pdf * Reflections and Refractions: https://graphics.stanford.edu/courses/cs148-10-summer/docs/2006--degreve--reflection_refraction.pdf * Music: https://raw.githubusercontent.com/SebLague/Misc-Project-Info/refs/heads/main/Coding-Adventures/FluidRendering Chapters: 0:00 Intro 0:27 Marching Cubes 05:58 Raymarching 10:40 Refract, Reflect, Fresnel 13:35 More Raymarching 18:28 A Simple Environment 20:40 Testing the Raymarched Fluid 25:03 Screen Space Technique: Depth Map 28:35 Simple Smoothing 33:42 Surface Smoothing 36:44 Rendering the Fluid 42:02 Spray, Foam, and Bubbles 55:12 Testing the Screen Space Fluid 57:22 Outro

Some small experiments with sound, and learning how to break signals down into their component frequencies by implementing the Discrete Fourier Transform. Support my work (and get early access to new videos and source code) on Patreon: https://www.patreon.com/SebastianLague Source Code: https://github.com/SebLague/Audio-Experiments/tree/Episode-01 Credits and References: ● @3blue1brown video: https://youtu.be/spUNpyF58BY?si=U5pu40UUNk-7mda0 ● Music: https://github.com/SebLague/Misc-Project-Info/blob/main/Coding-Adventures/FourierTransform Chapters: 00:00 Intro 00:48 Dot Wav 03:05 Waveform 04:24 Playing a Sound 05:03 Wave Simulation 10:31 Speed Change 12:38 Signal Generation 17:14 Fourier Vis (single frequency) 23:31 Fourier Vis (multiple frequencies) 28:01 First Attempt at DFT 31:39 The Nyquist Rate 35:14 Frequency Resolution 37:25 DFT Implementation 39:31 Testing the DFT Function 42:41 Outro

Attempting to render more intricate scenes using an acceleration structure called a Bounding Volume Hierarchy. Support my work (and get early access to new videos and source code) on Patreon or Nebula * Patreon: https://www.patreon.com/SebastianLague * Nebula: https://go.nebula.tv/sebastianlague Source Code: * GitHub: https://github.com/SebLague/Ray-Tracing Credits and References: * BVH Article: https://jacco.ompf2.com/2022/04/18/how-to-build-a-bvh-part-2-faster-rays/ * 3D Test Models: https://casual-effects.com/data/ * Music: https://github.com/SebLague/Misc-Project-Info/blob/main/Coding-Adventures/BVH.txt Chapters: 00:00 Intro 00:30 Triangle-Test Debug View 03:34 Bounding Boxes Inside of Bounding Boxes 04:41 Building a BVH 07:41 Traversing the BVH 09:13 GPU-Friendly Data 15:32 Converting Recursion to Iteration 18:06 Box-Test Debug View 21:42 Increasing the Depth of the BVH 25:11 Distance Test and Child Ordering 31:47 The Surface Area Heuristic 37:19 Speeding up the Construction 38:57 32-Byte Nodes 42:20 Transformations 45:10 Supporting Multiple Models 48:45 Some Tests and Final Thoughts

This... is text! Let's figure out how to draw it. Starring: Bézier curves and (oh so many) floating point problems. Support my work (and get early access to new videos and source code) on Patreon or Nebula * Patreon: https://www.patreon.com/SebastianLague * Nebula: https://go.nebula.tv/sebastianlague Source code: * GitHub: https://github.com/SebLague/Text-Rendering Credits and References: * Fonts and music: https://github.com/SebLague/Misc-Project-Info/blob/main/Coding-Adventures/TextRendering * https://developer.apple.com/fonts/TrueType-Reference-Manual/ * https://www.microsoft.com/en-us/research/wp-content/uploads/2005/01/p1000-loop.pdf * https://wdobbie.com/post/gpu-text-rendering-with-vector-textures/ Chapters 0:00:00 Intro 0:01:58 The Font Directory 0:04:27 Loading Simple Glyphs 0:10:42 Bézier Basics 0:13:42 The Character Map 0:15:47 Implied Points 0:18:11 Compound Glyphs 0:20:25 Size and Spacing 0:21:27 Rendering Glyphs with Lots of Triangles 0:22:17 Optimized Curve Rendering (Loop-Blinn) 0:28:20 A Brief Look at SDF Rendering 0:30:33 The Counting Method 0:31:48 Ray-Bézier Intersections 0:34:09 Point in Glyph Test 0:36:35 Shader Time 0:38:37 Floating Point Problems 0:41:22 The Evil Artifact Detector 0:45:36 The Closest Curve Method 0:50:48 Curve Splitting 0:54:31 Defeating the Evil Artifacts 0:58:58 Anti-Aliasing 1:02:47 Performance and Legibility 1:05:11 The Counting Method Returns 1:09:45 Outro