## These Beautiful Images are Created by Drawing Circles

The circle is the most important closed curve in the world. Also, it is the most symmetrical shape in the plane. In addition to these facts, it is interesting that we can create an unlimited number of beautiful images by drawing circles. In order to create a beautiful symmetrical shape by this method, I draw a family of circles which are defined by some mathematical formulas. So, it is very similar to the method I mentioned in my

6,000 Circles (I)

6,000 Circles (II)

6,000 Circles (III)

6,000 Circles (IV)

6,000 Circles (V)

8,000 Circles (I)

8,000 Circles (II)

10,000 Circles

20,000 Circles (I)

20,000 Circles (II)

4,000 Circles

This image shows 4,000 circles. For each k=1,2,3,…,4000 the center of the k-th circle is:

((2/3)(sin(6πk/4000))^3+(1/3)sin(26πk/4000), (2/3)(cos(6πk/4000))^3+(1/3)cos(26πk/4000))

and the radius of the k-th circle is:

(1/10)(sin(34πk/4000))^2+(1/12)(cos(136πk/4000))^4.

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