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**benice****Member**- Registered: 2010-06-10
- Posts: 110

My Gallery of Math Art: benice equation

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,420

it reminds me of the mandelbrot set.nice work benice!!!

btw,i have some ideas for you.see if this can be somehow used:Roulette

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,739

It is! Excellent job!

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,562

What are the ratios between the circles? I see the five pointed star.

**igloo** **myrtilles** **fourmis**

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**benice****Member**- Registered: 2010-06-10
- Posts: 110

Hi **anonimnystefy**,

Thanks for the link.

Hi **bobbym**,

You're welcome.

Hi **John**,

John E. Franklin wrote:

What are the ratios between the circles?

The ratios used in the eight animated GIFs on my blog post are

3, 3, 2, 2, 2, 2, 2.5, and 2.75 respectively.

My Gallery of Math Art: benice equation

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,739

Hi benice;

You are welcome, keep up the good work.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**benice****Member**- Registered: 2010-06-10
- Posts: 110

Hi All,

A few images of successive zooming in have been added in the original post.

My Gallery of Math Art: benice equation

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**Mrwhy****Member**- Registered: 2012-07-02
- Posts: 52

Great Stuff!

Can you add a way to halt the drawing so we can see how the wiggles are formed (the "stars" for example.

Did you find the wheel ratios by trial and error?

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**benice****Member**- Registered: 2010-06-10
- Posts: 110

Mrwhy wrote:

Can you add a way to halt the drawing so we can see how the wiggles are formed.

The animations are animated GIFs (not Flash videos).

Use a GIF animation software to see the static frame images.

Mrwhy wrote:

Did you find the wheel ratios by trial and error?

Yes.

My Gallery of Math Art: benice equation

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,739

Hi benice;

The one that consists of blue hexagons is a nice one!

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**Mrwhy****Member**- Registered: 2012-07-02
- Posts: 52

benice wrote:

Please explain what is going on here

The big circle is fixed?

The mid-size circle ROLLS on it without slipping?

OR

Is attached to it at a fixed point - while the big circle rotates

The small circle rolls on the mid-size circle? At what rate?

OR

The small circle is attached fixedly to the mid-size circle (which spins?)

OR

The small circle spins - at what rate?

The pen is attached to a fixed point

ON the small circle

OR

Within the small circle

Or rotates around the circumpherence of the small circle - at what rate?

Many thanks

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