These Beautiful Images Are Created By Drawing Circular Arcs

2016-02-04-1454611267-4539432-4000_Arcs_1.jpg

I have created the following images by thousands of circular arcs which are defined with trigonometric functions. Such families of arcs are very useful to introduce beautiful shapes. At the end of this post you can see the mathematical description of “6,000 Arcs (4)“. Also, in my previous posts you can see some images that I made by using

6,000 Arcs (1)

5,000 Arcs
2016-02-08-1454959402-99680-5000_Arcs_1.jpg

6,000 Arcs (2)
2016-02-06-1454756595-1732689-6000_Arcs_2.jpg

4,000 Arcs (2)
2016-02-05-1454668433-3141617-4000_Arcs_2.jpg

7,000 Arcs (1)
2016-02-04-1454592148-430801-7000_Arcs_1.jpg

3,000 Arcs (1)
2016-02-03-1454518196-7453920-3000_Arcs_1.jpg

3,000 Arcs (2)
2016-02-04-1454581776-8527064-3000_Arcs_2.jpg

7,000 Arcs (2)
2016-02-08-1454949666-605319-7000_Arcs_2.jpg

6,000 Arcs (3)
2016-02-08-1454953285-8149941-6000_Arcs_3.jpg

4,000 Arcs (3)
2016-02-07-1454864420-224662-4000_Arcs_3.jpg

6,000 Arcs (4)
2016-02-09-1455008563-668145-6000_Arcs_4.jpg
This image shows 6,000 circular arcs. For each k=1,2,3,…,6000 the endpoints of the k-th arc are

(S(k)cos(A(k))+X(k), S(k)sin(A(k))+Y(k))

and

(S(k)cos(B(k))+X(k), S(k)sin(B(k))+Y(k)),

and the following point is located on the k-th arc,

(S(k)cos(C(k))+X(k), S(k)sin(C(k))+Y(k))

where

S(k)=(1/20)+(6/15)(sin(32πk/6000))2,

A(k)=(214πk/6000)+(π/20)+(19π/20)(sin(32πk/6000))4,

B(k)=(214πk/6000)-(π/20)-(19π/20)(sin(32πk/6000))4,

C(k)=(214πk/6000),

X(k)=(21/19)cos(18πk/6000)+(21/38)(cos(34πk/6000))3,

Y(k)=(21/19)sin(18πk/6000)+(21/38)(sin(58πk/6000))3.

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