The collection of examples of things to draw with turtle graphics on this web site is widely influenced by things that are drawn with or influenced by math. Turtle Graphic excels at drawings that have traditionally been produce with a straight edge and compass. The collection of examples is here.

Arguably anything created with turtle graphics could be thought of as using math, since it uses numbers to express length, angles, counts and other attributes like color, width, and others. Mathematics itself studies tessellations (objects like tiles that fill a plane), geometric shapes (usually in two dimensions, but can be three or more), space filling curves, fractals, and various games. Some examples are here and here.

During the Golden Age of Islam (8th to 14th century), scholars developed knowledge in many fields including mathematics, science, art and architecture. One of the products is generally known as Islamic geometric art which uses figures drawn with a compass and straight edge to represent infinity. One form of Islamic geometric art is Girih which uses a set of geometric tiles to cover a plane and to create an intertwined strapping structure. The Islamic art of the Alhambra in Spain inspired M. C. Escher to “divide the plane” to find unusual shapes and figures that would tessellate. He also drew “impossible” objects that play with the mind’s view of various objects. A contemporary artist Steven Naifeh is inspired by the intersection of Islamic and western art.

Modern art includes minimalism and conceptual art, both of which were founded by Sol LeWitt. Conceptual art is where the concept of the artwork is a description and the implementation is left to draftsmen. The description is similar to an algorithm used by a computer to do some task.

Somehow I accidentally discovered vortex math, mainly by watching a You Tube video. The concept was simple enough and could easily be implemented in Turtle Graphics and results in some interesting graphics including some very unexpected daemons.

Art on a computer is represented by several formats. Which one is best depends upon what your needs are. This is discussed in JPEG-vs-PNG-vs-SVG.

Math and art

Art of Sol LeWitt

Sol LeWitt (1928-2007) was an American artist who inspired the minimalist movement and the conceptual art movement. Both of these are interesting for people trying to recreate his artwork on computers. Minimalist art tends to being simple. Conceptual art is art that is expressed as a set of directions which are then executed by someone else. The art work is conveyed with the instructions, not with the manifestation of those instructions.
Math and art

Art of Steven Naifeh

Steven Naifeh (1952-), artist, author, and businessman. Executed several art works which have been exhibited in various places around the world. These works in general are based on [Islamic geomentric patterns]. Some of his pieces were inspired by [Girih]. Gallery of Naifeh inspired art executed with Turtle Graphics Slide show of Naifeh inspired executed with Turtle Graphics
Math and art

Conceptural Art

Conceptual art focuses on the concept or idea of the art not the actual object. So the concept may be as simple as “a red wall,” but can be much more complex. Conceptual art was founded by Sol LeWitt. Part of his philosophy was founded by a early job of his as a draftsman (draughman) for the architect, I. M. Pei. In architecture the architect would come up with the concept of the building.
Math and art

Irregular Hexagon Tessellations

A tessellation is the tiling of a plane so that there are no gaps or overlaps. Usually only one geometric shape is used, like a triangle, square, or hexagon. Of course the easiest ways to do the tessellation is to use regular geometric shapes, ones where all sides are the same lengths, and to align the corners to maximize the symmetries. There is a class of tessellations that use irregular shapes.
Math and art

Islamic Geometric Patterns

Some Moslems believe that sacred art should not reflect nature, because nature is God’s work and cannot be improved upon. They let much of their sacred art be inspired by geometric patterns. While not all Islamic sacred art is geometric, there is plenty that is. There are many photos and tilings of Islamic Geometric Art on the Internet. One site is PatternInIslamicArt.com and another is Wikipedia.com/wiki/Islamic_geometric_patterns. These patterns are excellent examples of things that can be created with Turtle Graphics as they are generally created with a compass and straight edge.
Math and art

JPEG vs PNG vs SVG

Computers have different ways of handling graphic images. Each of these techniques have their own advantages and disadvantages. This page summarizes some of the important characteristics of common computer graphic formats. Tiff is the simplest image protocol in that it is just an array of the pixel values, where each pixel value represents the range of colors for image. This can be a single bit per pixel for black and white images or 24-bits to show the full range of red, blue and green components of the color.
Math and art

Vortex Math

Simple vortex diagram using modulo 9 and multiplier 2 to form the series 1, 2, 4, 8, 16 mod 9=7, 14 (or 32) mod 9 = 5, 10 ( or 64) mod 9 = 1 The concept of vortex math as presented by the You Tube Video seems simple enough. Just implement a function that plots a set of multiplier points evenly distributed around a circle and connections between point (n) and point (n+1) where point (n+1) = (n x multiplier) modulo modulus and point (0) = 1.