texture-synthesis VS WaveFunctionCollapse

We are at Embark! https://embark.dev/, https://embark.rs, https://embark.games.

Thank you! And yes, I agree. I was looking at uh https://github.com/mxgmn/WaveFunctionCollapse and wondering if that were applicable here :)

Have a good day!

Intuitively, it measures the difference between two probability distributions. It's not symmetric, so it's not quite that, but in my opinion, it's good intuition.

As motivation, say you're an internet provider, providing internet service to a business. You naturally want to save money, so you perhaps want to compress packets before they go over the wire. Let's say the business you're providing service to also compresses their data, but they've made a mistake and do it inefficiently.

Let's say the business has, incorrectly, determined the probability distribution for their data to be $q(x)$. That is, they assign probability of seeing symbol $x$ to be $q(x)$. Let's say you've determined the "true" distribution to be $p(x)$. The entropy, or number of bits, they expect to transmit per packet/symbol will be $-\sum p(x) lg(q(x))$. Meaning, they'll compress their stream under the assumption that the distribution is $q(x)$ but the actually probability of seeing a packet, $x$, is $p(x)$, which is why the term $p(x) lg(q(x))$ shows up.

The number of bits you're transmitting is just $-\sum p(x) lg(p(x))$. Now we ask, how many bits, per packet, is the savings of your method over the businesses? This is $-\sum p(x) lg(q(x)/p(x))$, which is exactly the Kullback-Leibler divergence (maybe up to a sign difference).

In other words, given a "guess" at a distribution and the "true" distribution, how bad is it between them? This is the Kullback-Leibler distribution and why it shows up (I believe) in machine learning and fitness functions.

As a more concrete example, I just ran across a paper talking [0] about using WFC [1] to asses how well it, and other algorithms, do when trying to create generative "super mario brothers" like levels. Take a 2x2 or 3x3 grid, make a library of tiles, use that to generate a random level, then use the K-L divergence to determine how well your generative algorithm has done compared to the observed distribution from an example image.

[0] https://arxiv.org/pdf/1905.05077.pdf

[1] https://github.com/mxgmn/WaveFunctionCollapse

wave function collapse studies - this is done with the https://github.com/mxgmn/WaveFunctionCollapse algorithm after I saw https://github.com/CodingTrain/Wave-Function-Collapse mention it. done in P5! IG https://www.instagram.com/ronivonu/

Inspiration and entropy propagation algorithm derived from https://github.com/mxgmn/WaveFunctionCollapse.

https://www.youtube.com/watch?v=Dfc-DQorohc

Craig Reynolds said the name "Boids" was inspired by The Producers Concierge scene, so that's how you should pronounce it:

Boids. Dirty, disgusting, filthy, lice ridden Boids. Boids. You get my drift?

https://www.youtube.com/watch?v=aL6mTMShVyk

The other really cool rabbit hole to explore for generating tiles and even arbitrary graph based content (I'm sold: hexagons are the bestagons!) is "Wave Function Collapse", which doesn't actually have anything to do with quantum mechanics (it just sounds cool), but is actually a kind of constraint solver related to sudoku solvers.

https://escholarship.org/content/qt3rm1w0mn/qt3rm1w0mn_noSpl...

Maxim Gumin's work: https://github.com/mxgmn/WaveFunctionCollapse

Paul Merrell's work:

https://paulmerrell.org/model-synthesis/

https://paulmerrell.org/research/

Oskar Stålberg's work:

https://twitter.com/OskSta/status/784847588893814785

https://oskarstalberg.com/game/wave/wave.html

There's a way to define cellular automata rules by giving examples of the before and after patterns, and WFC is kind of like a statistical constraint solving version of that.

So it's really easy for artists to define rules just by drawing! Not even requiring any visual programming, but you can layer visual programming on top of it.

That's something that Alexander Repenning's "AgentSheets" supported (among other stuff): you could define cellular automata rules by before-and-after examples, wildcards and variables, and attach additional conditions and actions with a visual programming language.

AgentSheets and other cool systems are described in this classic paper: “A Taxonomy of Simulation Software: A work in progress” from Learning Technology Review by Kurt Schmucker at Apple. It covered many of my favorite systems.

http://donhopkins.com/home/documents/taxonomy.pdf

Chaim Gingold wrote a comprehensive "Gadget Background Survey" at HARC, which includes AgentSheets, Alan Kay's favorites: Rockey’s Boots and Robot Odyssey, and Chaim's amazing SimCity Reverse Diagrams and lots of great stuff I’d never seen before:

http://chaim.io/download/Gingold%20(2017)%20Gadget%20(1)%20S...

Chaim Gingold has analyzed the SimCity (classic) code and visually documented how it works, in his beautiful "SimCity Reverse Diagrams":

>SimCity reverse diagrams: Chaim Gingold (2016).

>These reverse diagrams map and translate the rules of a complex simulation program into a form that is more easily digested, embedded, disseminated, and and discussed (Latour 1986).

>The technique is inspired by the game designer Stone Librande’s one page game design documents (Librande 2010). If we merge the reverse diagram with an interactive approach—e.g. Bret Victor’s Nile Visualization (Victor 2013), such diagrams could be used generatively, to describe programs, and interactively, to allow rich introspection and manipulation of software.

>Latour, Bruno (1986). “Visualization and cognition”. In: Knowledge and Society 6 (1986), pp. 1– 40. Librande, Stone (2010). “One-Page Designs”. Game Developers Conference. 2010. Victor, Bret (2013). “Media for Thinking the Unthinkable”. MIT Media Lab, Apr. 4, 2013.

https://lively-web.org/users/Dan/uploads/SimCityReverseDiagr...

Agentsheets: Alexander Repenning (1993–)

Interacting agents are embedded and interact within

I thought you were kidding but it's an actual thing!

https://github.com/mxgmn/WaveFunctionCollapse - Honorable mention, same guy.

Neat! This approach reminds me a lot of Wave Function Collapse.

Initial source of inspiration: https://github.com/mxgmn/WaveFunctionCollapse

It is actually a pretty new algorithm for procedural content generation. Check out this repo