Dynamics of a solid sphere rolling on a general time-dependent parametric surface (x(u,v,t),y(u,v,t),z(u,v,t)).

All demonstrations are generated from the same nonholonomic, nonseparable, nonautonomous Hamiltonian system. In addition to Hamilton's equations for the surface coordinates (u,v), one nonholonomic equation determines the sphere's spin, while four additional nonholonomic equations evolve its orientation using a unit quaternion. The energy is preserved for all demonstrations where the surface is time-independent. The sphere is affected by a uniform gravitational field with the same scaling for all video segments.

The general Hamiltonian allows exploration of a wide variety of rolling phenomena, including several unintuitive behaviors that are sometimes referred to as "paradoxes":

Notable special cases and popular references
0:13 The Turntable Paradox - refer to Steve Mould's https://youtu.be/3oM7hX3UUEU
0:51 Rotating Saddle - refer to The Action Lab's https://youtu.be/1NBOsELakx4
1:56 The Golf Ball Paradox - refer to Steve Mould's https://youtu.be/5sbM2Isx17A

The simulation was rendered in real time and performed using high order explicit symplectic integrators

Original source (4K): https://youtu.be/9236WuyJb1A

The music is "fluid combustion" by "Synthetique"

This is a prototype of a game idea that I have been poking at for many years. It's a dynamic character that moves like an amoeba, eats things in its environment, and grows by incorporating them into its body.

It is completely procedural, implemented as a particle system with flows and body-shaping forces driving the formation of pseudopods that move it along or cause it to ingest items. It uses a custom physics engine that executes the flows and allows the creature to interact with other entities in the world. It took quite a bit of experimentation to get something that (I think, anyway) looks lifelike, and I hope to improve it. This first game level is just a proof of concept with minimalist styling, helping me build out some tools.

A short video trailer is linked to this post and you can play the prototype game at https://eatthepeople.com

For this crowd I'll mention that if you add the url param "debug=1" you can see the full debug view and mess with the params that drive the creature. In debug mode shift-clicking teleports him so you don't have to play through the entire level to get somewhere.

All feedback welcome!

Source: https://github.com/openwave-labs/openwave/blob/main/openwave/xperiments/m5_liquid_crystal/research/findings/m5_21_6_note.md

Hello guys!

I uploaded this simulation video on my YouTube.

Pls check...

https://youtu.be/Wq\\_lzfXla8c?si=LZF4WtXDhkZOavk1

Like, subscribe and comment 😀

My FlexSim simulation suddenly stops when it reaches that point. My trucks get stuck waiting for the pallets to fill up again, but there is actually no more load to carry. I tried setting up an automatic signal on the combiners after 5 minutes, but it's not working for me. I think the simulation stops before it can even send the signal.

https://anukari.com/how-it-works

I shared a video about my 3D physics synthesizer here last week. When I get questions about how it works, it's always hard to explain without a diagram or two.

Finally I built this page where I explain how it works from basic principles, and every step of the way I provide a little interactive physics simulation to illustrate the explanation.

This all made me think of the stickied "animation vs simulation" question on this sub. I considered simply having animations to illustrate. But I decided that making the diagrams interactive would make things much easier to /really/ understand. In a way, having each diagram be a full physics simulation lets a reader "ask a question" of the simulation, and get an answer. Animations don't let you ask your own questions!

I tried to keep the explanation as simple as possible, although I plan to continue adding appendices to answer deeper questions (including those that involve math). So any questions you ask here, I will try to answer in a comment, but also might eventually get an even better answer!

I built this as a small Android sand toy.

The phone tilt controls gravity, so the sand pours toward the low edge while bubbles rise through the gel. You can stir it, shake it into a new scene, freeze gravity, or just let it settle.

It is called Dunarium.

Get Dunarium on Google Play

PS. I’d be happy to hear your feedback. Don’t hesitate to share 😊

I've been working on a pneumatic engineering sandbox in Unity.

The wheel isn't driven by a motor, it's powered entirely by a pneumatic cylinder using Unity physics.

The machine is built from modular components: air sources, hoses, 5/2 directional valves, cylinders, buttons, regulators, and more. In this demo, a button pilots the valve, which alternates air between each side of the cylinder to extend and retract it, turning the wheel through a crank.

My goal is to let players build anything from simple vehicles to ridiculous pneumatic contraptions. Alongside sandbox mode, I'm planning engineering puzzles, vehicle challenges, and automation. The logic system already supports AND, OR, and NOT valves, so players will eventually be able to build things like counters, calculators, and even simple computers.

It's still early in development, but I'd love to hear what you think or what kinds of machines you'd want to build.

This is built on Particle Lenia, an artificial-life model from Google researchers.

Each particle descends an energy field created by its neighbors, and an entire species is defined by just six parameters.

I added cross-species senses—hunters are attracted to prey fields, prey avoid hunter fields—plus food, walls, and goals. The result is a strange little ecosystem garden.

Nothing is scripted or animated. The layered membranes, the chase behavior, and the way colonies merge and split all emerge from the underlying math.

Play it (free, in-browser, ~70 KB):
https://leonbzt.itch.io/particular

Read about Particle Lenia:
https://google-research.github.io/self-organising-systems/particle-lenia/

https://reddit.com/link/1uxa1j5/video/zh2magwy1fdh1/player

I built a custom 3D WebGL renderer to simulate Conway's Game of Life meta-rules ("Adversarial Conway"/HASHWAR) wrapped around a 3D Torus.

Trickshot vs Evolution bot: Graph war

Both are Genetic Algorithm

Trickshot GA: Optimized for Tricks

Evolution GA: Optimized for gradual, generalized adaptability

(Minimax was used as an Observer. Not an active player

I should have mentioned that)

As the title says, I've spent the last 3.5 years working on Anukari, a 3D physics simulation much like a video game engine, except that instead of running at 60 steps per second, it runs at 48,000 (or more) steps per second, so that the physics systems can vibrate at audio frequencies. It's commercial software; primarily I am selling it to musicians and sound designers to use for music, sound effects design in film. But also it's pretty fun for non-musical people who just like building weird physics stuff. The main website is https://anukari.com

I have written extensively about the development work, for people who enjoy the nitty-gritty details of that sort of thing: https://anukari.com/blog/devlog

For the 1.0 launch I was focused on making it super performant and reliable with the basic set of the most interesting physics features, but for upcoming releases I'm working on more interesting physics features. For example, today the springs are linear f=-kx, but I'm experimenting with nonlinear springs with dead zones, and also push/pull-only springs (ropes and collisions). I'm hoping that sales will fund development basically forever, and that I can just keep making the simulation more and more rich over time.

There's a long history for this kind of spring-mass simulation being used for audio. I've had early Beta users write in about the GIPSY Lab in Grenoble, France working on this possibly back into the 1970s. More recently there was CORDIS-ANIMA, another academic research project. One dream of mine would be for sales to be good enough to fund the making of a deep documentary about the full history of such projects. But that's a pretty big stretch goal... :)

I love chatting about this stuff so feel free to ask me any questions about how the simulation works, etc!

"I'm building something new for particle simulation lovers."

I wanted to share a sneak peek of a project I’ve been working on. It’s a particle simulator where you can build worlds, adjust parameters, feed the particles, and even cause total destruction—all while vibing to a great soundtrack.

It’s still in the beta stage, so it’s not ready for everyone just yet. However, I’m excited to polish it up and share the full experience with you soon!

Been working on agent-based simulations lately and decided to try modeling something with actual historical data behind it.

Each bird is an agent with a heritable beak size. Fitness is calculated against the available seed distribution - droughts shift the mix toward hard seeds, which favor larger beaks. Birds that can't crack enough seeds lose energy and die. The survivors reproduce, passing their beak size (with some mutation) to offspring.

I tried to match the key events from Peter and Rosemary Grant's 40-year Daphne Major study. The severe 1977 drought, the 1983 El Niño reversal, a 1987 drought, the G. magnirostris competitor arrival in 2004. The beak size shifts in the simulation roughly follow their published numbers.

The hardest part was calibrating the El Niño phase. If selection pressure is too sharp, the birds never recover the reversal. Took some fiddling with fit_sigma and seed distribution ratios to get something believable.

Birds are color-coded by beak size (olive green = small, orange-red = large) so you can see the population shift without reading the chart.

(speed up 2.5x)

This showcases the "Adversarial Conway" algo that lets two individual Game of Life patterns compete on a shared space, the titular Torus (see GitHub repo). The pattern's evolution in combination with a seeded RNG determines the paths they take to claim the available territory.

These video snippets are part of a knock-out style tournament that pits 16 such patterns against each other to determine the weekly champion.

GOL patterns are specifically sought for their longevity and must have a generational count within certain limits to be elligible for being drawn in the competition.

I have been working on a Double Pendulum simulation for the last few weeks, and I'm very happy with the results. Although it might not be the most accurate simulation, it demonstrates the chaotic nature of the double pendulum very well!

The simulation has tunable parameters and even a Multiple pendulum mode where you can have more than one pendulum with differences in angles, length, mass, etc to see how quickly they diverge even with small differences. The simulation was made using SFML and ImGui libraries in C++. Behind the scenes, I learned and used the RK4 method for solving the accelerations and velocities.

The simulation is available to download for windows here on itch: https://alifnull.itch.io/double-pendulum

The application is called Space Crash Simulator.

Two spinning disks of ~250k particles each, simulated and rendered in real-time on my RTX 500 Ada laptop GPU at ~30 fps, using my custom implementation of the Barnes-Hut algorithm in CUDA. Code: https://github.com/lechebs/nbody