Drawing Mathematical Flowers With Trigonometric Functions!

Drawing Mathematical Flowers With Trigonometric Functions!
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Flowers are symbols of beauty, love and happiness. Trigonometric functions enable us to draw beautiful mathematical shapes that resemble flowers. Below are some instances which I made by drawing circles, ellipses and circular arcs. At the end of this post you can see the mathematical description of "9,000 Circles".

8,000 Circles
2016-05-01-1462123095-8840341-8000_Circles_Flower.jpg

10,000 Circles
2016-05-01-1462128061-3292095-10000_Circles.jpg

8,000 Ellipses
2016-05-04-1462389492-3431870-8000_Ellipses.jpg

8,000 Arcs
2016-05-03-1462257926-1413449-8000_Arcs.jpg

6,000 Ellipses
2016-05-05-1462444135-6183639-6000_Ellipses.jpg

10,000 Arcs
2016-05-03-1462263437-7992174-10000_Arcs.jpg

9,000 Circles
2016-05-05-1462464601-1010880-9000_Circles.jpg

This image shows 9,000 circles. For each k=1,2,3,...,9000 the center of the k-th circle is (X(k), Y(k)) and the radius of the k-th circle is R(k), where

X(k)=cos(14πk/9000)(1-(3/4)(sin(20πk/9000))-(1/4)(cos(60πk/9000))),

Y(k)=sin(14πk/9000)(1-(3/4)(sin(20πk/9000))-(1/4)(cos(60πk/9000))),

R(k)=(1/120)+(1/18)(sin(60πk/9000))+(1/18)(sin(160πk/9000)).

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