## These Beautiful Images Are Created by Drawing Squares

In order to create beautiful images by drawing squares, it is very useful to use

16,000 Squares (1)

16,000 Squares (2)

7,000 Squares

6,000 Squares (1)

6,000 Squares (2)

10,000 Squares (2)

10,000 Squares (3)

10,000 Squares (4)

10,000 Squares (5)

16,000 Squares (3)

This image shows 16,000 squares. For each k=1, 2, 3, … , 16000 the vertices of the k-th square are:

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

where

X(k)=sin(10πk/16000)(cos(18πk/16000))2,
Y(k)=(cos(14πk/16000))3,
A(k)=(1/400)+(1/25)(cos(64πk/16000)cos(192πk/16000))12+(1/70)(cos(192πk/16000)cos(384πk/16000))10+(1/120)(cos(384πk/16000)cos(1152πk/16000))10.

16,000 Squares (4)

This image shows 16,000 squares. For each k=1, 2, 3, … , 16000 the vertices of the k-th square are:

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

where

X(k)=sin(10πk/16000)(cos(14πk/16000))2,
Y(k)=cos(14πk/16000)(cos(10πk/16000))2,
A(k)=(1/400)+(1/12)(cos(14πk/16000)cos(42πk/16000))12+(1/30)(cos(96πk/16000)cos(192πk/16000))12+(1/60)(cos(192πk/16000)cos(384πk/16000))10.

See more images at: mathematics.culturalspot.org & http://www.ams.org/mathimagery/thumbnails.php?album=40.

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