### regular polygon and mandelbrot

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#### guitard

• Fractal Freshman
• Posts: 3

#### regular polygon and mandelbrot

« on: February 21, 2018, 12:02:59 PM »
inside the circular-shaped bulb, is it known that the secondary bulb coincides with regular poligons?
forget the right part that does not correspond to anything.
maybe the number of bulb comes from the regular polygon.
cordially,
Thomas.

« Last Edit: February 21, 2018, 12:22:14 PM by guitard »

#### lkmitch

• Fractal Fanatic
• Posts: 28

#### Re: regular polygon and mandelbrot

« Reply #1 on: February 21, 2018, 07:05:53 PM »
I believe so. The boundary of the secondary disk is a perfect circle, centered at (-1,0) with radius of 0.25. The disks on its boundary are tangent to the circle with angles of 2*pi*m/n, where m and n are coprime integers and n corresponds to the periodicity of the disk (relative to the secondary disk). For example, there are six sub-disks with periodicity of 14 (7 for the sub-disk x 2 for the secondary disk). The tangent points are at angles of 2pi/7, 4pi/7, 6pi/7, 8pi/7, 10pi/7, and 12pi/7 (relative to the center). Since the radius is constant, these tangent points are the vertices of a regular polygon.

#### guitard

• Fractal Freshman
• Posts: 3

#### Re: regular polygon and mandelbrot

« Reply #2 on: February 21, 2018, 11:32:54 PM »
ok

#### guitard

• Fractal Freshman
• Posts: 3

#### Re: regular polygon and mandelbrot

« Reply #3 on: February 22, 2018, 11:33:38 AM »
it should have a bulb at the place of the red circle? no?
but I am not yet able to guess the size of the bulb.

Ok i guess the size of the next circle that should draw the next bulb by logic it should be 3 times bigger, it encompasses all the mandelbrot.
I put red dash to see the little visible circle.

Cordially.
so we can imagine the mandelbrot continue infinitely bigger also.

« Last Edit: February 22, 2018, 01:57:06 PM by guitard »

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