These Beautiful Images Are Created By Drawing Ellipses

We can create an unlimited number of beautiful images by drawing ellipses. The following images are some examples that I have created by some computer programs. At the end of this post you can see the mathematical descriptions of "Butterfly" and "6,000 Ellipses (3)".

8,000 Ellipses (1)
2015-11-10-1447155493-3061905-8000_Ellipses_1.jpg

6,000 Ellipses (1)
2015-11-10-1447155619-9430548-6000_Ellipses_1.jpg

Ring
2015-11-10-1447155683-6298082-Ring.jpg

9,000 Ellipses (1)
2015-11-10-1447155762-3972557-9000_Ellipses_1.jpg

8,000 Ellipses (2)
2015-11-10-1447155865-6713934-8000_Ellipses_2.jpg

9,000 Ellipses (2)
2015-11-10-1447155949-5959918-9000_Ellipses_2.jpg

12,000 Ellipses
2015-11-10-1447156035-6686789-12000_Ellipses_1.jpg

8,000 Ellipses (3)
2015-11-10-1447156107-9632152-8000_Ellipses_3.jpg

6,000 Ellipses (2)
2015-11-10-1447156164-2096560-6000_Ellipses_2.jpg

9,000 Ellipses (3)
2015-11-10-1447156238-7126963-9000_Ellipses_3.jpg

Butterfly
2015-11-10-1447156309-1961063-Butterfly.jpg
This image shows 8,000 ellipses. For each k=1,2,3,...,8000 the foci of the k-th ellipse are:

A(k)+iB(k)+C(k)e^(300πik/8000)

and

A(k)+iB(k)-C(k)e^(300πik/8000)

and the eccentricity of the k-th ellipse is D(k), where

A(k)=(sin(14πk/8000))^3,

B(k)=sin(14πk/8000)sin(10πk/8000),

C(k)=(1/200)+(1/20)+(1/20)cos(22πk/8000),

D(K)=(199/200)-(1/7)(sin(22πk/8000))^8.

6,000 Ellipses (3)
2015-11-10-1447156361-3806880-6000_Ellipses_3.jpg
This image shows 6,000 ellipses. For each k=1,2,3,...,6000 the foci of the k-th ellipse are:

A(k)+iB(k)+C(k)e^(200πik/6000)

and

A(k)+iB(k)-C(k)e^(200πik/6000)

and the eccentricity of the k-th ellipse is D(k), where

A(k)=cos(16πk/6000)cos(6πk/6000),

B(k)=sin(16πk/6000)cos(6πk/6000),

C(k)=(1/200)+(1/14)+(1/14)(sin(10πk/6000))^3,

D(k)=(49/50)-(1/7)(sin(6πk/6000))^2.

See more images at: mathematics.culturalspot.org.