Using the Sawtooth Wave to Create Some Beautiful Images

2015-10-24-1445684262-7312869-9000_Circles_1.jpg

When we want to create a beautiful image by drawing line segments or circles, we can use

4,000 Line Segments (I)

4,000 Line Segments (II)
2015-10-27-1445954760-6276651-4000_Line_Segments_2.jpg

7,000 Circles (I)
2015-10-24-1445681668-5827114-7000_Circles_1.jpg

3,000 Line Segments (I)
2015-10-24-1445686145-7220703-3000_Line_Segments_1.jpg

3,000 Line Segments (II)
2015-10-27-1445945144-1141679-3000_Line_Segments_2.jpg

3,000 Line Segments (III)
2015-10-26-1445880474-3385479-3000_Line_Segments_3.jpg
This image shows 3,000 line segments. For each k=1,2,3,…,3000 the endpoints of the k-th line segment are:

(S(20k/3000)cos(2πk/3000), S((18k/3000)+(1/2))(sin(2πk/3000))^3)

and

(S(16k/3000)(cos(2πk/3000))^3, S((14k/3000)+(1/2))sin(2πk/3000)).

7,000 Circles (II)
2015-10-26-1445879717-1853933-7000_Circles_2.jpg
This image shows 7,000 circles. For each k=1,2,3,…,7000 the center of the k-th circle is:

(S((14k/7000)+(1/2))sin(10πk/7000), S(14k/7000)cos(10πk/7000))

and the radius of the k-th circle is:

(1/400)+(1/9)(S(14k/7000)cos(50πk/7000))^2.

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