Program to generate really really large circle of life diagram?

[carrie]

Hi,
does anyone know a program to generate a really really large circle of life diagram with approx 2,000 or 3,000 or 10,000 circles?

it would be nice if it generates 3-dimensional spheres instead of 1-dimensional circles.

[Questioner]

I don't know what a circle of life diagram is. Do you have an example of a small one?

[Lavazza]

AKA "Flower of Life" ?

[carrie]

yes, a really big one with approx 1000 circles or 5000 circles.

The thing is not big enough.

[Peregrinus]

Like a Mandelbrot?

[carrie]

> Like a Mandelbrot?

Something like that, but this is more straight forward.

something that can draw few thousand circles and lay it out in some way the image can be manipulated.

Preferably in 3-dimensions.

[AnthroHeart]

That sounds like a script would be needed for 3D Studio Max, Maya, Blender, or similar 3D program.

They would need to follow a certain algorithm, depending on the pattern you are talking about.

By 3D, wouldn't you mean using spheres instead of circles?

[Questioner]

Carrie, it looks to me that the image you presented could be made with an algorithm something like this:

Number of rings = 3.
Size scaling factor = 100 (just an arbitrary guess).

Create the large circle:
Large circle center = center of the drawing space.
Large circle radius = number of rings * size scaling factor.
Draw the circle.

For i = 1 to number of rings. For each ring:
Number of circles in this ring = 6 * (i-1), but never less than 1 circle in a ring.
Angle increment in this ring = 360 / number of circles in this ring.
Distance increment in this ring = size scaling factor / number of rings.
For each circle in this ring:
Center of the circle is determined as an offset from the center of the large circle.
Clockwise angle is next angle increment, starting with 0.
Center of the small circle is distance increment for this ring away from center of the large circle.
Draw the circle.
Continue until all circles are drawn in this ring.
Continue until all rings are drawn.

By setting a larger constant for the number of rings, you should get more inner circles.

Why not try putting this into code and play around with it? I think I'm on the right track for the 2D version. Once that works then it will need to be scaled up/extruded into placing spheres in 3D space rather than circles in 2D space. This will require a further loop inside each ring, so that the angle is a (azimuth, elevation) pair for each next sphere.

[Lavazza]

I could possibly write a script to create something like this in the 3D program Maya, if that would be helpful. Unfortunately the major roadblock for me is not having enough time.. Looks like a fun project. When you say you would like it to be 3D though, what do you mean? An array of 3D spheres may not look much like the illustration above.

[Questioner]

Lavazza, closely packed 3D spheres would produce a 2D cross section through the middle that looks just like the original picture.
The Wikipedia article on this includes the math:
http://en.wikipedia.org/wiki/Close-packing_of_spheres

[Lavazza]

Yes, but in order to see the pattern you would have to view the mass of spheres orthogonally, and if you're doing that there is no purpose for creating the image with spheres, you may as well use circles. The only reason you would wish to use spheres would be to view it in a perspective or non-ortho view, which would only show the flower of life pattern at chance angles if at all. Most of the time you would only see a mass of tightly packed spheres. I believe?

[Questioner]

Lavazza, carrie's a 3D virtual world developer working on a way to model the Law of One as a 3D game. I suspect that her ultimate use of this will be included in her game.

[Lavazza]

Ah, I see! In that case this becomes even more tricky. It would be cool to have the player try and find the magic spot to sit where the array of spheres lines up in to the flower of life pattern, but there are technical hurdles involved in this. Having a few thousand spheres in a video game might be taxing on the game hardware- especially when we consider that each sphere needs to be high enough resolution in itself to support a nice round shape. Proceed with caution here!

[AnthroHeart]

If we are doing circles in 3D space, then how are the circles aligned? They have to fit on some sort of plane, be it orthogonal or such.

If we are showing a 2D representation of it, I don't see a point in doing in 3D.

In 2D, circles are represented with the equation: x^2 + y^2 = r^2
at the origin.

When we add offsets for plotting more circles we get:
(x - h)^2 + (y - k)^2 = r^2

Spheres are really simple primatives, so with decent hardware, 1000 of them shouldn't tax the processor. Some GPUs are capable of millions of vertices per second as far as I'm aware.

[Questioner]

The spheres would be plotted in 3D space as a composite object made up of smaller objects. They would all be positioned as an offset relative to the center of the packed group.

The whole area of computing power for the masses is fascinating to me. I hope carrie won't mind my having a digression here. She's probably better up to date on much of this than I am anyway and might be able to correct my mistakes.

3D graphics power available to consumers these days is astounding. For a few hundred dollars, a GeForce 8800 card can shade and overlap more than 3 million triangles a frame at 60 frames per second. With 1,000 spheres shown at once, this would be 3,000 triangles per sphere, each just a few pixels across. Each pixel would have whatever colors most beautifully represent a smoothly drawn surface. The 3D engine runtime would adjust the level of detail in a surface depending on how much it fills the screen.

With a card like that driving an HDTV, you'd never see any kind of angles or seams, just the impression of a thousand smooth spheres - with moving lights shining through fog and smoke, if you like.

High-end consoles like Playstation 3 and Xbox 360 have somewhat less powerful graphics engines. But the consoles include custom processors, system architectures and operating systems designed to easily manipulate massive amounts of realtime data for 3D simulations.

I haven't tried to run a benchmark, but I suspect that most ordinary desktop and laptop computers have a powerful enough graphics chip to give a pretty good rendering of a thousand close-packed spheres. They might only be able to do flat lighting, and show some seams and jagged edges. But you'd be able to figure out at a glance that you're looking at spheres, and probably spin and zoom them in realtime at 30+ frames per second.

For about a decade, high-end gamers have been the main source of improvements in consumer-level computers. If it wasn't for their desire to navigate photorealistic 3D virtual world models in realtime, there would be little reason to buy anything beyond a year-2000 level machine. That was when pretty much every machine for $500 and up became powerful enough to do all the office work that most people needed, with the machine mostly waiting around for the user to think of something to type.

Unless you're compiling a large program, crunching a very large spreadsheet, creating audio or video or photos, trying to turn off the dancing paper clip and search dog, or getting rid of spam, when was the last time you ever had to wait more than a few seconds for your computer to do anything you asked?

Within a few years, even netbooks, PDA's and tablets will have the same power as today's desktop machines.

I think within a decade, the question of whether a machine is powerful enough for 3D rendering will make as much sense as asking today if a computer is powerful enough to show different types of fonts. That was a serious issue when the 128KB, 8 MHz Mac was introduced, but is now something we can take for granted - usually, even on phones. As Moore's law and consumer electronics industry continue their magic, 3D will be more and more affordable until it's just thrown in for free to pretty much everything.

I think that Neil Stephenson's description from Snow Crash (a very trippy novel) is an astute prediction: Using any old computer, you'll be able to see a good enough version of a 3D virtual world to navigate and enjoy. A sign of luxurious wealth will be to add gratuitous photo-realastic rendering, especially of difficult to model materials such as flowing water and leaves. In the same way that wealthy entities show off with their buildings now, in the future they'll show off with spectacular renderings that they create and show to you that your own little machine couldn't create on its own.

When I have time to post my Smalltalk series here, I hope to trace that all the way up through Open Cobalt. As far as I know, this is the closest anyone's come to building Stephenson's "Metaverse" out of entirely free software. Unlike the novel, we have an opportunity to use free software tools that put the power of understanding and changing the system in the hands of ordinary users. Another generation or two and modifying this code will be an everyday skill for everyone, just as most of us already know how to fry an egg and to type. I'm almost done with my first Smalltalk post about how I believe its designers used Law of One principles in its foundation, and hope to post that within a week or so.

Sorry about hijacking the thread, back to the circle algorithm. As you can tell, this is stuff I've been thinking about a lot.

[AnthroHeart]

Unfortunately I have Vista. It takes 5 mins to boot, about that long to shut down. And FireFox was at a crawl, often freezing up. There is no spyware or virii (I've used 3 different scanners).

Vista is just a memory and harddrive hog.

But back on topic, instead of setting a limit of 1000, if we're talking about being able to zoom in forever, and out forever, there should be no bounds. It would be a self-contained repeating algorithm. Kind of like a recursive loop.

Unless you're compiling a large program, crunching a very large spreadsheet, creating audio or video or photos, trying to turn off the dancing paper clip and search dog, or getting rid of spam, when was the last time you ever had to wait more than a few seconds for your computer to do anything you asked?

[carrie]

Upgrade to Windows v7. I upgraded and never looked back.

[carrie]

hi,
Some update:

The circle of life needs to be viewed in 3-dimensions. If you see it in 3-dimensions, it looks like the inner structure of a base of base of a base of a base of the building block of an atom.

It works by circles encapsulating circles:
0, 1,
4, 64,
216, 512,
1000, 1728, 2744, 4096,
5,832, 8000, 10,648, 13,824,
17,576, 21,952, 27,000, 32,768
and so on

1 circle joins with 3 other circles to form 4 circles (1 base, 3 new)
4 circles are surrounded by 60 other circles to form 64 circles (1 base, 3 (level 1), 60 (level 2)) = 64
64 circles are surrounded by 156 other circles to form 216 circles (level 3=156)
... form 512 circles (level 4=296)
... form 1,000 circles (level 5=488)

but there's problem. The circles cut off the sides at level 4:
at level 4 (216), it cannot hold to 8 circles (1 circle at each side of the cube)
at level 5 (512), it cannot hold to 24 circles (3 circles at each side of the cube)
at level 6 (1000), it cannot hold to 50 circles (6.25 circles at each sides)
1000-82 = 918 circles.

If you have 918 circles in a cube formation, you notice it looks almost spherical.

The circle travels through three-dimensional smaller mesh which permits where it goes. (It goes by vector transformations) though each unit of time.

[carrie]

Is it just me or is this similar to law of squares?