Dynamic Spirograph - Circle Rolling around Rolling Circle

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Dynamic Spirograph - Circle Rolling around Rolling Circle

Postby benice on December 11th, 2011, 2:24 am 

Circle Rolling around Rolling Circle (1)

Circle 1 rolls around inside of the fixed base circle.
Circle 2 rolls around inside of Circle 1.

Image
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Re: Dynamic Spirograph - Circle Rolling around Rolling Circl

Postby Fuqin on December 11th, 2011, 3:52 am 

I used to love Spirograph when I was a kid; you could buy sets with cogged wheels pencil positions and a range of shapes for those who don’t know, I found them quiet hypnotic, the pattern presented in this one kind of lets me imagine how a moon orbiting a planet orbiting a sun that is orbiting a bigger sun might be seen to travel, that if you can picture a sun dead center of the green circle.
there is an interpretative one here
http://www.mathplayground.com/Spiromath.html
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Re: Dynamic Spirograph - Circle Rolling around Rolling Circl

Postby benice on December 11th, 2011, 1:21 pm 

Hi Fuqin,

Thank you for your suggestions. I will try to explore the four-planet case.

Merry Christmas and the best wishes for 2012!

benice
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Re: Dynamic Spirograph - Circle Rolling around Rolling Circl

Postby Fuqin on December 11th, 2011, 1:59 pm 

Thank you for your suggestions. I will try to explore the four-planet case.

Hay it wasn’t a suggestion , I was merely saying that it reminded me of something like that I’m an artist at my core so I just love graphical information , but hay , have fun and go for it.
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Re: Dynamic Spirograph - Circle Rolling around Rolling Circl

Postby Laconic Lethality on December 20th, 2011, 11:04 am 

Interesting, appears almost chaotic in nature. Try the bunimovich stadium as well, I still wonder what can be possible through the application of chaos. Merry Christmas to all,
http://en.wikipedia.org/wiki/Dynamical_billiards
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Re: Dynamic Spirograph - Circle Rolling around Rolling Circl

Postby benice on January 9th, 2012, 11:46 pm 

Circle Rolling around Rolling Circle (2)

Circle 1 rolls around inside of the fixed base circle.
Circle 2 rolls around outside of Circle 1.



Hi Laconic Lethality,

Thank you for the link to the wiki page on dynamical billiards.
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Sumo Wrestler

Postby benice on January 9th, 2012, 11:50 pm 

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Re: Dynamic Spirograph - Circle Rolling around Rolling Circl

Postby BioWizard on January 11th, 2012, 11:36 am 

Is the speed of rotation of a the two smaller circles constant? My guess would be that it's not constant for the inner circle, but my intuition might be wrong.
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Re: Dynamic Spirograph - Circle Rolling around Rolling Circl

Postby benice on January 12th, 2012, 1:00 pm 

BioWizard wrote:Is the speed of rotation of a the two smaller circles constant?

Hi,

Yes, all speeds are constant in above posts. I also explore the cases with non-constant speeds.
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Re: Dynamic Spirograph - Circle Rolling around Rolling Circl

Postby benice on January 27th, 2012, 5:12 pm 

Circle Rolling around Rolling Circle (3)

Circle 1 rolls around outside of the fixed base circle.
Circle 2 rolls around inside of Circle 1.


Circle Rolling around Rolling Circle (4)

Circle 1 rolls around outside of the fixed base circle.
Circle 2 rolls around outside of Circle 1.
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Re: Dynamic Spirograph - Circle Rolling around Rolling Circl

Postby benice on January 27th, 2012, 5:15 pm 

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Re: Dynamic Spirograph - Circle Rolling around Rolling Circl

Postby Jordan on January 27th, 2012, 7:07 pm 

That's pretty neat benice, it reminds me of the Mandelbrot set.
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Re: Dynamic Spirograph - Circle Rolling around Rolling Circl

Postby kluge on January 28th, 2012, 3:32 am 

Just wondering, what is the Benice Equation to which you keep referring?
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Re: Dynamic Spirograph - Circle Rolling around Rolling Circl

Postby benice on January 29th, 2012, 6:59 pm 

Hi Jordan,

You're welcome.


Hi kluge,

It means that I find or make fun pictures using mthematical equations or inequalities.

Example pictures:
BFE, Monster Cow, Chubby Girl, Starflakes, Antlerman, Demon Sheriff, Pink Sissy

An example (monster) equation is given here.
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Happy Valentine's Day

Postby benice on February 9th, 2012, 6:30 pm 

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