Turing's papers on the subject formed part of the research for my dissertation project, which culminated in a Matlab simulation of the skin patterns he described with inhibitors/activators.
I recently converted it to JS and also Ruby, as an excuse for a few coding exercises. It's still a work in progress, but can be found here:
Since you're in the field, maybe I could ask about your impression of Wolfram's NKS? As a layperson, I understand it's a generalization of many classes of such patterns.
Actually, the dissertation project was my only experience with the field. Although I read some of NKS at the time, it's a distant memory and so I wouldn't be able to say!
Really interesting guy and the book covers a whole host of areas where self-organising systems shape organisms without necessarily much genetic intervention
Cool. It's fun to see how Turing patterns are everywhere in biology. However, as Turing himself said (allegedly): 'Well the stripes are easy, but what about the horse part?'
Having developed an amateur interest in cell biology over the last few years, the single most interesting thing I've learned is that Interglobulin-M cells cells just happen to have same basic morphology as the kind of animals that they come from.
I'm so sorry, I should have written immunoglobulin-M and didn't notice my mistake. I don't feel qualified to recommend a text, I just follow references from here.
That explains what the central dogma is, but not how specific patterns of gene expression lead to a horse. That's something that's still quite a mystery. Hell, even after a lot of work, we don't still entirely know how even something as simple as Drosophila does its segmentation.
I feel like this pattern is a great example of how mathematicians, scientists, and technologists should focus their attentions on things that are economical and 'good enough' rather than fetishizishing ever-increasing levels of precision.
While, say, calculating fundamental constants to the nth degree of precision is fun and intellectually satisfying in many respect, the marginal utility of each additional digit of precision asymptotically approaches zero so it's really a self-indulgent luxury. But this fetishizing of precision also has drawbacks; it misdirects resources and effort into improvements whose benefits fall far short of the costs.
You wouldn't use a laser pointer to explore a room. Of course you could; but mapping a topological space using LIDAR is only possible because we have computers to do the vast amount of number crunching required, and it's only very recently that we've gone from very sparse representations to ones of sufficiently high resolution to give us representations that are immediately recognizable as familiar spaces.
I will take fast proximity over slow exactitude any day of the week; I want models that get me close enough with very few parameters rather than more perfect ones that require a thick book's worth of specifications to articulate.
Unfortunately, this is more a generalized problem of human disbelief in the unlikely than anything specific to science. We can't really say, 'scientists now have to be more receptive to weird ideas'.
I recently converted it to JS and also Ruby, as an excuse for a few coding exercises. It's still a work in progress, but can be found here:
https://github.com/rai-hi/rails-skin-patterning
Demo here:
https://skin-simulator.herokuapp.com/