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Author Topic: Sphere collision diagrams  (Read 1117 times)
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matsoljare
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« on: August 11, 2013, 03:08:55 PM »

Has anyone ever tried using simple sphere collision algorithms, or other physical simulations to produce fractals?

Here's one example of what i mean. Consider a typical simulation of a pool table break, as found in many games. Consider the position of one of the balls at the end of the break, it could be any of them, or several. The final position is dependent on a highly complex series of events, including multiple collisions.

Now change the angle (or possibly the strength) of attack very slightly, and the final position of that ball will be different in a highly unpredictable way. Map out the final position of the ball for a continous series of different angels, and the result should have some fractal properties. I picture it to be a somewhat spirograph-like pattern, or something similar to the ripple functions that are occasionally discussed on here.

I hope this is clear enough for you to understand what i mean. Do you know if it has been tried, or can anyone here make a simple simulation themselves?
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cKleinhuis
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« Reply #1 on: August 11, 2013, 03:28:45 PM »

in fact i am going to visualise something similar for the upcoming mandelbrot introduction, showing the effects of slight changes in a 3 body simulation, rendering the pathes of a few seconds of simulation time, and then animate slight changes and show how the pathes utterly change heavily the longer the simulation runs ... too bad i am thrown back 2 monthes from the series i plan wink

a complex situation like a pool table, just changings of positions in the micro-promille area of starting position of just one single ball will change the results heavilly!!!!!!!!!!!!!! this is chaos cheesy
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matsoljare
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« Reply #2 on: August 11, 2013, 04:31:45 PM »

Yeah, i'm thinking if anyone can use the routines from a existing pool game, or some public domain algorithms that are available, that would make that part considerably easier. It doesn't even need to be realistic in any way, i'm just interested in what kind of patterns it would make.
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cKleinhuis
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« Reply #3 on: August 11, 2013, 05:55:36 PM »

here is a sequence of images i created for my recent speech in mexico,

it is a 3 body simulation, without collision, decreasing the time step more and more,
after that you see the simulation for 10 seconds running, the area that is formed
is called a "attractor", if it is fractal we also call it "strange attractor" the chaotic
behaviour of this simulation can be seen by the fact that nearly every position on
the attractor is beeing visited over time

this is basically what i am preparing for the mandelbrot introduction i am working
on, it serves as the introduction for deterministic chaos ...


here you go:
the first image shows a large time step of 0.01 seconds , and one second of simulation time
 

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cKleinhuis
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« Reply #4 on: August 11, 2013, 05:58:53 PM »

in this picture a far smaller time step is used, which gives a better approximation of the "reality"
decreasing time step even further does not yield many more changes here a time step of 0.00001 is used, as
well simulating for 1 second, the black rounded circles mark the starting positions, the white ones the position
of each after 1 second

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cKleinhuis
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« Reply #5 on: August 11, 2013, 06:02:56 PM »

here you see a time step of 0.00001 but this time running for 10 seconds, you see the attractor is forming,
the starting position is very unlikely to be reached again


* gravity100secondsNormalMass.jpg (74.37 KB, 800x600 - viewed 61 times.)
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cKleinhuis
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« Reply #6 on: August 11, 2013, 06:05:08 PM »

in this picture we have the same set up with just one slight change, the blue particle now has 1percent more
mass, the movement has changed ....


* gravity100seconds_1percentmoremass.jpg (72.04 KB, 800x600 - viewed 58 times.)
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cKleinhuis
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« Reply #7 on: August 11, 2013, 06:07:28 PM »

and here the setup with a 50 percent mass increase for the blue particle.....


* gravity100secnds_50percentmoremass.jpg (66.36 KB, 800x600 - viewed 58 times.)
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matsoljare
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« Reply #8 on: August 11, 2013, 06:12:59 PM »

Yeah, what i'm thinking off is rendering multiple versions of the same collision, changing the angle (or velocity) just slightly each time, and marking only the final placement of each (or every) ball.
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cKleinhuis
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« Reply #9 on: August 11, 2013, 06:21:02 PM »

since the position is very chaotic, the change of ending position is very harsh,
i have not the equipment right now to render more, but believe me the next tutorial issue
i am releasing will feature some nice animations of what you are talking about, simulating
for 100 seconds, while changing starting conditions wink stay alert!
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matsoljare
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« Reply #10 on: August 12, 2013, 12:20:24 AM »

Yeah, i believe if the angle change is just small enough, partial continuity will be achieved. Another option is of course to vary the velocity instead of the angle, or the position of one of the balls, or even the walls.
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cKleinhuis
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« Reply #11 on: August 12, 2013, 06:50:10 AM »

as far as i experienced, the changes have to be ridicilous small something
like 0.00000001 change of just one single parameter to be "smooth"
nevertheless, you brought my attention to another aspect, ( this will at sometime be
covered as well, but let me just describe what i mean )

the other aspect of "chaotic" behaviours is that at some point they become ridicoulusly
stable, for example the hurricane on the jupiter, or a simple water wave in a river, that
can be used for surfing, i wonder if that can be visualised/achieved through a particle simulation
as well, consider a e.g. rotating cloud of particles, and when throwing a relatively big
ball at it, the whole system should behave just like before, still changed, but the overall
attractor shall remain nearly unchanged ... this is described in the book chaos, that
chaotic systems become very very stable at some point, for example the soliton waves
which relate to tsunami waves as well ...

as soon as i have my full fledged core i7 ready, i am going to make more tests and visualisations,
perhaps using more particles, and perhaps even with collision features, i will think of this thread
when getting my hands on it again providing you some toy to play around, but it takes at least
2 more monthes from now....
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matsoljare
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« Reply #12 on: August 12, 2013, 09:03:21 PM »

Have you tried actually making any diagrams yet? What are you using?
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cKleinhuis
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« Reply #13 on: August 12, 2013, 09:32:32 PM »

lol, its my own software with just a basic numerical solver for gravitational movement wink
hmm, so, you really want to push me ?! i will see if i can create a diagram of resulting
positions ... lets see...

arr. i am sorry, right now i am too tired, and the equipment i am using here is not a nice development environment sad (4:3 small screen + laptop sad )
« Last Edit: August 12, 2013, 09:46:01 PM by cKleinhuis » Logged

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JosLeys
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« Reply #14 on: August 12, 2013, 11:46:51 PM »

Two billiard tables with 50 balls. Identical starting positions except for one ball.
See what happens in this movie at time 6:30 : http://www.chaos-math.org/en/film
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