Maurer rose

Let r = sin(nθ) be a rose in the polar coordinate system, where n is a positive integer. The rose has n petals if n is odd, and 2n petals if n is even. We then take 361 points on the rose: : (sin(nk), k) (k = 0, d, 2d, 3d, ..., 360d), where d is a positive integer and the angles are in degrees, not radians. ==Explanation==

A Maurer rose of the rose r = sin(nθ) consists of the 360 lines successively connecting the above 361 points. Thus a Maurer rose is a polygonal curve with vertices on a rose. A Maurer rose can be described as a closed route in the polar plane. A walker starts a journey from the origin, (0, 0), and walks along a line to the point (sin(nd), d). Then, in the second leg of the journey, the walker walks along a line to the next point, (sin(n·2d), 2d), and so on. Finally, in the final leg of the journey, the walker walks along a line, from (sin(n·359d), 359d) to the ending point, (sin(n·360d), 360d). The whole route is the Maurer rose of the rose r = sin(nθ). A Maurer rose is a closed curve since the starting point, (0, 0) and the ending point, (sin(n·360d), 360d), coincide. The following figure shows the evolution of a Maurer rose (n = 2, d = 29°). ==Images==

The following are some Maurer roses drawn with some values for n and d: ==Example implementation==

Using Python: import math, turtle screen = turtle.Screen() screen.setup(width=800, height=800, startx=0, starty=0) screen.bgcolor("black") pen = turtle.Turtle() pen.speed(20) n = 5 d = 97 pen.color("blue") pen.pensize(0.5) for theta in range(361): k = theta * d * math.pi / 180 r = 300 * math.sin(n * k) x = r * math.cos(k) y = r * math.sin(k) pen.goto(x, y) pen.color("red") pen.pensize(4) for theta in range(361): k = theta * math.pi / 180 r = 300 * math.sin(n * k) x = r * math.cos(k) y = r * math.sin(k) pen.goto(x, y) ==References==