“The wing veins of the fruit fly Drosophila melanogaster have long been studied as an example of how signaling gradients in a growing tissue can generate precise, reproducible patterns…”
^ this line from Hoffman and Donoughe’s paper “A simple development model…” makes me think I should read more research on this. How much of what I’m doing has already been done?
Focus. (-:
I’ve got the curvature matching the leading edge of the wing using one set of parameters and I’ve got it matching the rest of the primary veins using another set of parameters. Let’s see about matching them both using a single set of parameters.
The “root segment dir” parameters don’t need to change at all. That’s the direction of each segment at the base of the primary vein. Those look good. It’s what happens after that so I’ll remove those sliders from the panel for now.
And I’ll add sliders for the parameters I mentioned yesterday.
a * index^2 * generation^2 + b * index^2 * generation
+ c * index * generation^2 + d * index * generation
I won’t worry about names for now, that’s probably 80% procrastination.
Procrastinating on Parameter Searches #
I seem to procrastinate when I’m about to do a bunch of parameter tweaking. I guess I’m afraid that exploring the space is going to be slow and painful and may not even produce the desired result. Sounds ripe for training an AI model to learn the parameters instead but of course that’s got its own set of issues.
I guess that’s why I made those grids of reaction diffusion outputs: it’s a way of exploring the parameter space without tweaking parameters endlessly.
Huh. I just realized that for reaction-diffusion I used a grid whereas with the insect wings I’ve used a bunch of sliders. I could theoretically use a grid here, too, but it doesn’t fit the problem quite as well. The output for reaction-diffusion takes a long time to generate so I like to run a bunch of them while I do something else and check the output later. With the insect wings the output is generated immediately so I can just tweak the parameters on the fly and get a feel for the parameter space very quickly.
But this is eight more parameters we’re talking about!
Parameter Search #
I think I’ve found reasonable bounds for each of the four parameters. I’m tempted to bind a key to randomize each of the parameters. Then I can just press it over and over again until I get something close and tweak from there.
Before I go with the spray and pray method, let me at least try to wrap my head around what each of these parameters is doing.
Reference image. I’m starting from where the curve matches the leading edge.
Low a.x.
High a.x.
Low a.y.
High a.y.
Low b.x.
High b.x.
Low b.y.
High b.y.
Low c.x.
High c.x.
Low c.y.
High c.y.
…aaand I can’t tweak the ’d’ parameters because there are just too many. They’re off the bottom of the screen.
Hiding the alpha sliders for now. (-:
Low d.x.
High d.x.
Low d.y.
High d.y.
So prettay.
You can see the up-down vs. left-right changes difference between the x and y parameters pretty clearly. Let’s group them based on those two categories.
x-parameters #
Low a.x.
Low b.x.
Low c.x.
Low d.x.
The curves for a.x and c.x are more extreme, they fold back on themselves. The curves for b.x and d.x on the other hand are gentler and maintain an affect like diagrams of magnetic fields.
This makes sense since the a and c parameters have the squared generation term. So those values will change very quickly as it moves from the base to the tip of the primary vein.
a * index^2 * generation^2 + b * index^2 * generation
+ c * index * generation^2 + d * index * generation
y-parameters #
The same pattern holds for the y-parameters. I won’t include all the images here, you’ll just have to load it up and play with it yourself. (-:
Low a.y.
More observations #
When the parameter value is low I get effects that change very quickly. When it’s high it seems to slowly converge and not change very much. Haven’t wrapped my head around that just yet. Maybe that’s just a result of my parameter ranges..? Or maybe the values for “Segment Dir” linear and quadratic terms that I’m using as a baseline?
a * index^2 * generation^2 + b * index^2 * generation
+ c * index * generation^2 + d * index * generation
Oh, the b and d terms affect the first curve—the curve nearest the root—and the a and c terms affect the second curve. That follows because a and c both have generation^2 which means the impact will be much greater near the tip than near the root.
We’re getting somewhere.
I can expect something similar for the terms with index and index^2. So.