These Beautiful Images Are Created By Drawing Rectangles

2016-03-18-1458335514-3015996-5000_Rectangles_1.jpg

Mathematical formulas enable us to create an infinite number of beautiful images. Below are ten mathematical images which are made by trigonometric functions. I just used high-school level mathematics to create them. At the end of this post you can see the mathematical description of “7,000 Rectangles (2)“.

5,000 Rectangles (1)

10,000 Rectangles (1)

6,000 Rectangles (1)
2016-03-19-1458415857-2543913-6000_Rectangles_1.jpg

6,000 Rectangles (2)
2016-03-20-1458477263-2472137-6000_Rectangles_2.jpg

10,000 Rectangles (2)
2016-03-23-1458760006-8782727-10000_Rectangles_2.jpg

7,000 Rectangles (1)
2016-03-24-1458824284-102286-7000_Rectangles_1.jpg

5,000 Rectangles (2)
2016-03-24-1458826534-5014249-5000_Rectangles_2.jpg

10,000 Rectangles (3)
2016-03-24-1458834834-1814877-10000_Rectangles_3.jpg

10,000 Rectangles (4)
2016-03-24-1458836135-4449962-10000_Rectangles_4.jpg

7,000 Rectangles (2)
2016-03-24-1458839123-1494583-7000_Rectangles_2.jpg

This image shows 7,000 rectangles. For each k=1, 2, 3, … , 7000 the vertices of the k-th rectangle are:

(X(k)-A(k), Y(k)-B(k)),

(X(k)+A(k), Y(k)-B(k)),

(X(k)+A(k), Y(k)+B(k)),

(X(k)-A(k), Y(k)+B(k)),

where

X(k)=((1/4)+(3/4)(cos(πk/700))2)sin(2πk/7000),

Y(k)=((1/4)+(3/4)(cos(πk/700))2)cos(2πk/7000),

A(k)=(1/200)+(1/7)(cos(84πk/7000))8,

B(k)=(1/200)+(1/7)(sin(82πk/7000))8.

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