These Beautiful Images Are Created by Drawing Squares

2015-12-13-1450015462-5246327-10000_Squares_1.jpg

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

16,000 Squares (1)

16,000 Squares (2)
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7,000 Squares
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6,000 Squares (1)
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6,000 Squares (2)
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10,000 Squares (2)
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10,000 Squares (3)
2015-12-14-1450124653-385195-10000_Squares_3.jpg

10,000 Squares (4)
2015-12-17-1450360518-7890436-10000_Squares_4.jpg

10,000 Squares (5)
2015-12-17-1450365401-9971589-10000_Squares_5.jpg

16,000 Squares (3)
2015-12-17-1450367321-4459788-16000_Squares_3.jpg
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)
2015-12-17-1450370383-4596064-16000_Squares_4.jpg
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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