Using primes, I constructed some polygonal lines of interesting shapes. The inclination angle of each section of the polygonal line follows a simple function including primes. Starting with prime 3, I took one thousand primes to create polygonal lines with one thousand sections. By variation of one parameter, different polygonal lines can be generated each with different patterns of very specific characteristics.

Lines are combined with special functions to generate colorful surroundings.

Turtle geometry is applied to create different kinds of beautiful symmetric objects looking like stars or snowflakes. The change of inclination angles of lines follows some prescribed rules. Lines are combined with special functions to generate colorful surroundings.

In 1960, Peter McMullen draw by hand this wonderful representation of the Gosset polytope 4_21 (described in 1900). The set of vertices form the root system of the exceptional Lie group E8 (this is why it is also called the E8 polytope). More recently, John Stembridge draw a computer image, from which we have been inspired to make this hand made thread version.