<p>It looks like a <a href="https://en.wikipedia.org/wiki/Voronoi_diagram" rel="noreferrer">voronoi diagram</a> with a non-Euclidean distance metric. Probably not <a href="https://en.wikipedia.org/wiki/Taxicab_geometry" rel="noreferrer">Manhattan L1</a> but something close related, but maybe <a href="https://en.wikipedia.org/wiki/Mahalanobis_distance" rel="noreferrer">Mahalanobis</a> with some kind of restriction on seed point generation and movement.</p>

<p>A similar result may be calculated with <a href="https://link.springer.com/article/10.1007/s10707-006-0006-8" rel="noreferrer">Weight-proportional Space Partitioning Using Adaptive Voronoi Diagrams</a> when reducing spatial resolution of the domain. </p>

<p>I guess yo'll find similar examples in <a href="https://www.shadertoy.com/" rel="noreferrer">ShaderToy</a> if you look for voronoi examples, which code you could study, and could be much simpler than the algorithm in the paper. </p>

CC BY-SA 4.0
2019-01-18T23:30:13.483Z
This looks very close to what I was looking for thank you! Question though, is there a related formula on how to achieve the rectangular effect for each node? From what I've looked into it seems like all examples have voronoi diagrams with polygons. The weight-proportional paper had a rectangular image on google but this paper is paywalled.
Sosa
CC BY-SA 4.0
2019-01-18T07:12:06.727Z
2019-01-18T07:12:06.727Z
David
<p>Is there a name for this type of effect where many area sizes are increased/decreased in relation to each other? I'm looking for some type of algorithm, formula, logic, etc. for recreating this. Here is the effect (which I believe was created in After Effects):</p>

<p><a href="https://i.sstatic.net/3cYuP.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/3cYuP.gif" alt="The Tatami Galaxy (Yojouhan Shinwa Taikei / 四畳半神話大系) - Clear END"></a></p>

<p>Source: <a href="https://www.youtube.com/watch?v=ewICfFjc4CI" rel="nofollow noreferrer">The Tatami Galaxy (Yojouhan Shinwa Taikei / 四畳半神話大系) - Clear END</a></p>

CC BY-SA 4.0
2019-01-18T16:46:48.617Z
I think perhaps it might be "constraint-based" or "rule-based" modelling. 

Ivan Sutherland's sketchpad program (https://en.wikipedia.org/wiki/Sketchpad) perhaps may have been the first.
Simon F
<algorithm><animation>
What algorithm is used in this animation from Tatami Galaxy?
Sosa
# What algorithm is used in this animation from Tatami Galaxy?

(Asked by: username_0 on 2019-01-17)

Is there a name for this type of effect where many area sizes are increased/decreased in relation to each other? I'm looking for some type of algorithm, formula, logic, etc. for recreating this. Here is the effect (which I believe was created in After Effects):

[![The Tatami Galaxy (Yojouhan Shinwa Taikei / 四畳半神話大系) - Clear END](https://i.sstatic.net/3cYuP.gif)](https://i.sstatic.net/3cYuP.gif)

Source: [The Tatami Galaxy (Yojouhan Shinwa Taikei / 四畳半神話大系) - Clear END](https://www.youtube.com/watch?v=ewICfFjc4CI)

**Tags:** algorithm, animation

> **Comments:**
> **username_1**: I think perhaps it might be "constraint-based" or "rule-based" modelling.   Ivan Sutherland's sketchpad program (https://en.wikipedia.org/wiki/Sketchpad) perhaps may have been the first.  

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## 1 answers

### Answer by username_2 on 2019-01-18. Score: 7 | Accepted answer

It looks like a [voronoi diagram](https://en.wikipedia.org/wiki/Voronoi_diagram) with a non-Euclidean distance metric. Probably not [Manhattan L1](https://en.wikipedia.org/wiki/Taxicab_geometry) but something close related, but maybe [Mahalanobis](https://en.wikipedia.org/wiki/Mahalanobis_distance) with some kind of restriction on seed point generation and movement.

A similar result may be calculated with [Weight-proportional Space Partitioning Using Adaptive Voronoi Diagrams](https://link.springer.com/article/10.1007/s10707-006-0006-8) when reducing spatial resolution of the domain.

I guess yo'll find similar examples in [ShaderToy](https://www.shadertoy.com/) if you look for voronoi examples, which code you could study, and could be much simpler than the algorithm in the paper.

> **Comments:**
> **username_0**: This looks very close to what I was looking for thank you! Question though, is there a related formula on how to achieve the rectangular effect for each node? From what I've looked into it seems like all examples have voronoi diagrams with polygons. The weight-proportional paper had a rectangular image on google but this paper is paywalled.  

---

