And my attempt at using Poisson-disc sampling to generate stippling patterns in real time in a GPU shader: http://gregschlom.com/devlog/2015/01/31/stippling-effect-scr...
I wish my blog post had more details on the technique, but basically I am pre-computing Poisson-disc distributions at several (255) density levels in such a way that the samples are adaptive (ie: all samples from levels 1-n are also samples at the level n+1.
I'm then storing that information in a texture, and reading from it in a shader to know whether or not to draw a stipple.
The tricky part is to figure out how to do that on arbitrary 3D surfaces.
I wrote some Python scripts to calculate Ripley's K-function, which looked like a good way of quantifying this:
But she didn't think the distribution was as interesting as i did, and never used them!
I'd bet math phobia.
People working in Biology usually are not Math savy and are proud of it. Many of them are there to run away from other scientific Math intensive fields.
Anyone suggesting anything along this lines will be immediately shut down just because of that.
Like in the article the paper referenced below openly speculates about the use of organizational structures like this.
Edit: Sorry, this was written from my phone.
Relevant paper: http://onlinelibrary.wiley.com/doi/10.1002/dneu.22281/abstra... (use scihub)
1) Hyperuniform materials can be transparent - and have direction independent band gaps - http://arxiv.org/pdf/1510.05807v3.pdf
2) You can induce irreversible hyperuniformity in some emulsions by shaking them at certain amplitude - http://arxiv.org/abs/1504.04638
Surely there is an opportunity for some DIY garage physics here :)
Absolutely fascinating, and it's applications in materials are amazing. Whatever-direction bandpass filters? Crazy cool.
Old growth forest that did not get planted by humans have a much more chaotic distribution that's influences by fires, fallen trees, local fauna, and competition for sunshine with other trees.
According to their theory: "(...) the average distance between the trunks of individuals (trees) of the same size scales linearly with radius (of the tree)"
In the forest they measured, the fractal shape of the tree actually extended to the forest itself, as if the forest itself is one big "tree" with actual trees as its branches.
(Though, trees are 3D fractals, forest is a 2D plane, how does that work?..)
Some trees also secrete chemicals that block their offspring from growing over their roots, which can combine with light availability to further the minimum distance between large trees.
and for a D3 animated example: https://bl.ocks.org/mbostock/dbb02448b0f93e4c82c3
... Stuff like this makes me want to throw everything away and study math fulltime. That's still an option if I ever get FU money. Be sure to click through to the related article about the (spoiler) meteorite fragment containing a quasicrystal.
crystalline structures have lower entropy compensated by increase in the entropy of the environment due to heat being transferred out of crystalline structure during its formation.
It is kind of intuitively obvious that hyperuniform(random) forest have higher entropy than crystalline style ordered forest would have. I don't see connection to environment (like heat transfer in crystal case) that would allow to compensate for decrease of entropy in an ordered forest.
So I'm not surprised you get a hyperuniform distribution. It's not truly random, because there's a pull towards maximum packing density in one direction, balanced by a push towards a spatial expansion distribution around each tree in the other.
Intuitively, I'd suspect this pull/push balance explains most hyperuniform distributions.
Also known as the principle of least action