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Author Topic: Plenty of Orbits  (Read 1920 times)
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Althir
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« on: April 01, 2010, 08:34:57 PM »

A little background:
I was bored and therefore coded a small program that would display the orbit of an object around another. Then I was even more bored (boreder?) and added another object orbiting the first object. The graphic output is of course nothing against the images I have seen here even in the short time I have been here,but you get the idea. Because the visualisation looked a lot like a Mandelbrot (if you can't see it in the picture below it is because it doesn't anymore - that was just a programming error), I added more and more (in total 14) levels, as well as an option to zoom and change the quality settings. The picture below is Level 14 with a quality setting of 200.

This thing contains symmetry along the X-axis as well as some kind of self-similarity (though you might think different on that one)


This is a zoom to a point on the left, just below the symmetry axis. The biggest of these... tumors (hehe) is actually just a single pixel in the first image, same quality settings, 100x zoom.

Considering I stumbled across this on accident, it is fairly cool.

This thing is also the reason why I even registered here: I wanted to ask if anyone knows this thing (which is not all too unlikely, considering how generic my approach was) and can tell me a formula I could enter in Xaos to look at a cooler looking version of it that does not need three minutes to render a single picture (stupid engine limitations. If I didn't hate Java I'd remake it there, it's a lot faster than GM.)
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Timeroot
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« Reply #1 on: April 02, 2010, 12:12:56 AM »

Any system with 3 planets moving is chaotic - if you trace out the line one planet makes, it's a strange attractor. When you say "levels", do you mean that you had 14 planets? Cause that would be pretty intensive!

P.S. - If you want to speed your program (I don't know if you've done this or not) there pretty simple little tricks that let you reduce the quality (is this your timestep?) without sacrificing accuracy. Mind sharing your code with us? wink
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
Althir
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« Reply #2 on: April 02, 2010, 12:29:29 AM »

I don't think you'd get the code, actually. It's not an actual language such as Python or whatever others there are, it is the scripting language that comes with a software called "Game Maker".
What you see there is an object orbiting an object orbiting an object... bla. The circle in the center does not stand for the orbit of the first object, but for the center object all others revolve around.
I could even give you a compiled .exe of that thing, but the controls are... whew. 'td take too long to write a documentary. One can en- and disable the orbits of the objects one by one, which is admittingly cool.

The quality setting actually only defines how far one object goes before recalculating the angle. So Level 1 in quality 2 already looks like Level 1 in quality 400. You can clearly see the orbit of object 14 (then even being a smooth curve rather than edgy) with a 200x zoom with quality setting 400.

This is the most recent shot, with the newest version of that program, with a minimap (so that one knows about when the part one is in will be rendered) and also mouse controls, which obviously can't be seen in the shot.
Holy Odin, I just had a minor epiphany. I could write a simple check as to whether any of the planetary objects is on screen and if not drastically lower the quality, which would speed things up. A lot.

If I find the time, I'll write a documentation as to how to control this thing and compile you an exe, alright?
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Pauldelbrot
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pderbyshire2
« Reply #3 on: April 02, 2010, 01:55:42 AM »

If I didn't hate Java I'd remake it there, it's a lot faster than GM.)

Try Clojure. All the power of the JVM plus all the power of a Lisp, minus all the bondage-and-discipline and baroque syntax of Java. Downside: some of the usual ones for a Lisp. All the parentheses. And prefix math notation. The really big typical-Lisp-drawbacks, lack of a decent library and lack of a decent editor, are nonissues though, as Clojure code has access to any Java library code (any Java at all, including your own Java classes, and anything else you can invoke from Java, such as Jython or JNI-invoked C) and there's a Netbeans plugin for Clojure. Another frequent Lisp issue, proprietary compilers and language extensions, is also lacking: Clojure is open source, Netbeans and the plugin are open source, and Java is being open sourced. There are strong open source JVMs and Java libraries out there already. So you wouldn't be locking yourself into a closed system.
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makc
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« Reply #4 on: April 02, 2010, 01:59:04 AM »

I once made triple pendulum simulator tracing its locus but it didn't appear to be any more complex than double pendulum. There's that problem, if every orbit radius is smaller than previous one, you have increasingly small detail that are hard to see; and if radii are nearly same, you can't really tell one orbit details from another.
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Althir
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« Reply #5 on: April 02, 2010, 01:45:46 PM »

Increasingly small detail? I thought that was the point! That's why I implemented zoom in my program!
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makc
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« Reply #6 on: April 02, 2010, 02:46:51 PM »

well they are fine on their own, but I was thinking about seeing all of them in one shot. maybe some color-coding "black" area according to curvature of nearest "white" point would allow us to "see" small details, just like colored Mandelbrot exterior allows us to see otherwise invisible parts of set?
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Timeroot
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« Reply #7 on: April 02, 2010, 10:05:24 PM »

Ohhhh wowwww Ifeeldumb.  head batting I get it: you're not actually doing Newtonian gravity and simulating the differential equations, you're assuming they're locked in circular orbits - it's like the planet is level 0 (the circle in the center), then the moon is level 1, and the moon's moon is level 2, and the moon's moon's moon is level 3... more like the pendulum than actual gravity. In light of that, this is a very nice design! How did you choose the lengths of the specific orbits? Was it just arbitrary, or was it something specific, like a geometric sequence? And are they always rotating at a constant rate, or are you accounting for everything like conservation of angular momentum and what-not?

More pics!  grin
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
Althir
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« Reply #8 on: April 02, 2010, 10:39:35 PM »

It's a fairly early vision and I suck at physics. The rotational period and altitude is static for all objects. Level 1 has an altitude of 430px in zoom 1, that is because before I added the zoom feature I wanted it to fit on the screen entirely. Level 1 has 64px, Level 2 32px and so on, so the altitude is decreasing by 50% with each level, whereas the orbital period is 50% shorter for every level. That means if the planet takes ten seconds to rotate around the central object, the moon takes five seconds to rotate around the planet.

This is basically how it looks like for every level, just that further levels orbit other objects themselves. The relative orbit to the reference is always the same.

If I ever find out how I might add eccentricity to the orbits to add some variation, or add planets with retrograde motion or something. Though I'd need half a dozen Sheldon Coopers to get everything right. Actually, if I had half a dozen Sheldons, this would become an accurate simulation in which the moon's moon's moons are affected by the mass of the moon and shit. But, as I pointed out, I suck at physics. One of the first subjects I wiped off my schedule, right before Latin and history.
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Pauldelbrot
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pderbyshire2
« Reply #9 on: April 02, 2010, 10:48:18 PM »

Who the hell is Sheldon Cooper? I've heard of Einstein, Newton, and the like but this Sheldon's not on any of my famous-scientists lists. Or my famous-mathematicians lists.
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Althir
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« Reply #10 on: April 02, 2010, 10:51:34 PM »

A character from a TV show. Google it. It kicks butt.
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kram1032
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« Reply #11 on: April 02, 2010, 11:41:25 PM »

this looks neat cheesy
hmm...
could you do a phase and/or frequency shift over iterations? smiley
that would possibly break symmetries or create nice variations of the shapes.
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Althir
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« Reply #12 on: April 02, 2010, 11:42:53 PM »

You mean like changing the orbital periods and/or altitude of the objects?
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Timeroot
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« Reply #13 on: April 03, 2010, 03:04:31 AM »

police Okay, people, stop jabbering about pointless stuff with orbits and whatever.... let's talk about the important thing:

You quit Latin?!??!?!??? It's the best language ever! It's true that I might be biased because we always spend about half the class talking about junk, like racism, this one hobo who ran for mayor and everyone loved (sadly, he did not win), and our own little localized memes. Oh, and we make fun of the vegetarian Jew in our class (not seriously though), and this one "dumb" kid who, although he is by far not the dumbest, makes the dumbest comments by far (most of the other not-so-bright students are reallllly quiet...). And the teacher brings us cookies. But despite all this, I really like Latin, the way you have pieces separated so nicely that you just take apart and put back together again in English... it's so much more like a computer!!! <3

^ If anyone is unhappy about that little rant of fun, my excuse is this: "Other users, please don't do this, try to stay on topic. I did this as an example of what not to do."  evil

Anyway, this sounds really cool. The shape of your level 2 curve - that is, of a moon - is that of a prolate or curtate (depending on the speed) hypocycloid. On very rare occaisions, it will be a prolate or curtate epicycloid; only one of the 171 moons in our solar system, I think, follows the path of an epicycloid. I read a bit about Kepler's laws, which provide polar coordinates for the motion of a planet in an ellipse. Apparently, the exact position at a time can't be calculated exactly - it's involved the solution of a transcendental equation. Just including a bit of code to approximate it should do, though.

One thing I would like to see is a moon with orbital radius 1/2, which is being orbited by a moon with orbital radius with 1/3, followed by 1/4, followed by 1/5, etc.... obviously their orbits would have to be out of sync, so a phase shift of 1 radian could probably throw them off enough to make things interesting.
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
Althir
Guest
« Reply #14 on: April 03, 2010, 03:48:41 AM »

I think you mix up the radius and the orbital period, you probably want to change the time the moon takes to finish an orbit rather than how far it is away. This is actually controlled by two different variables.
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