Drawing Mathematical Flowers With Trigonometric Functions!

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))4-(1/4)(cos(60πk/9000))3),

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

R(k)=(1/120)+(1/18)(sin(60πk/9000))4+(1/18)(sin(160πk/9000))4.