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[BWG]

Hi there
Here is a screenshot from my WIP game Neoglobin:



The green and white mess shows the agents that are selected and the red circles show the target positions for those agents after giving a move command.
The challenge was to find a nice distribution for the points in a circle, so they wouldn't all bunch up once they got there.

As you can see from the image, I found a nice solution and I thought it might be of interest to people.

It is based on the packing of sunflower seeds. It's quite interesting actually and relates to fibonacci series and the golden ratio.

More info here.

Anyway, so that's what I did and it worked out rather well. I also wrote a little program in processing to experiment with it:

Code:

size(512, 512);
background(0);
smooth();

for (int i=0; i<600; ++i)
{
  float ang = 1.61803399*2.0*PI*i;
  float r = sqrt(i+1)*10;
  float x = width/2 + sin(ang)*r;
  float y = height/2 + cos(ang)*r;
  ellipse(x, y, 10, 10);
}

Please let me know if you find it useful or if you have ever used it before. I'd be interested to see what other uses can be made for it.

Cheers

[Mattivc]

Looks interesting. I think i will play around with this algorithm a bit later. Thanks for sharing.

Its kinda fun to think about, that some equivalent of this mathematical function lies somewhere within a sunflowers DNA.

Hmm, it might be interesting to use this for the tiles to a turn-based strategy game or something. Something other than grid or hexes

[mokesmoe]

Hexes would technically be packed better, but this probably fits a variable amount of circles better.

Its kinda fun to think about, that some equivalent of this mathematical function lies somewhere within a sunflowers DNA.

If you have a bunch of points that all repel each other and put them in the middle one at a time this pattern will form naturally. There's nothing fancy in the sunflowers DNA. Sorry to ruin your dreams.

[FibonacciSpaghetti]

Nice, I always loved that illustration of the math, but I've never seen it simply put before. May have to play around with it some time.

[Sir Wolf]

Its kinda fun to think about, that some equivalent of this mathematical function lies somewhere within a sunflowers DNA.

If you have a bunch of points that all repel each other and put them in the middle one at a time this pattern will form naturally. There's nothing fancy in the sunflowers DNA. Sorry to ruin your dreams.

I thought that was the point - not the specific about sunflower, but the fact that the pattern will form naturally. That a mathematical function describes such a natural pattern. That math is such a natural thing. It indeed is kinda fun to think about.

[BWG]

If you have a bunch of points that all repel each other and put them in the middle one at a time this pattern will form naturally. There's nothing fancy in the sunflowers DNA. Sorry to ruin your dreams.

Yeah. There's a great book from Biran Goodwin called "how the leopard changed its spots" and a much earlier book by D'Arcy Thompson, "on growth and form" (one of my all time fave books).
They both discuss how physical constraints and environmental interaction dictate the shape of a growing organism just as much as DNA. Very interesting stuff.

[Prinsessa]

Wow. Thanks for sharing. I have no idea when this could prove useful to me, but it's pretty. Bookmarked it.

[Maud'Dib Atreides]

I was reading something somewhere once where this can really come in useful.

To make a "slime ball" like in GISH is simple, just do like this:

(1) put a number of particles in a circle
(2) connect neighboring particles with Hooke's law damped springs, forming a rubberband
(3) calculate the area of the polygon formed by the particles using this equation
(4) set that area as the slime's rest area
(5) for each loop calculate the slimes new area using the same equation
(6) calculate slime pressure p = k * (area - rest area), where k is a stiffnes coefficient
(7) apply a normal ("inwards" / "outwards") pressure force to each particle pair
( voila, now your slime actsas a peace of jelly!

All sorts of modifications can be made, but this is the gist of the idea. I might have a code sample lying around (BASIC dialect and C dialect), I'll post it if I fall over it.

Cheers,
Mike

http://www.gamedev.net/topic/621866-slime/

The thread was about the physics of a 2D Slime.