I developed several programs using software called "Processing 3" (freely available Java-based mathematics graphics software), to allow me to realise precision drawings of the ideas I was coming up up with in my notebooks. I added some controls to change the overall size of the designs, the darkness and thickness of the grey construction lines, etc. It was initially felt that a background of appropriate construction lines would give a better sense of the accuracy of the designs. I also added some line extensions that extended out beyond the actual design, so that one could see where the main lines were positioned behind large areas of solid black. The line extensions as well as the background of construction lines were later felt to be not necessary.

As part of the image captures shown below is a black box to the left of the designs with about 6 lines of writing. The parameter controllers were positioned above this writing and are not captured as part of the screen captures used. The 6 lines of writing in the left black box are the values of the parameter controllers, and they were printed to the screen so that they are captured along with the designs.

With each screen capture made with my Processing 3 programs, a Scalable Vector Graphic (SVG) file is also saved along with the image file. These SVG files can be loaded into a vector graphics program, such as Adobe Illustrator or InkScape, and be enlarged to any size you would like, with no degradation in line quality. They could be printed out as posters or billboards and still have very clean sharp lines.

It is exciting seeing the precision and geometry of these images.

A simple design, based on drawing 4 black triangles around the four corners of the large square, over a drawing of grey 'construction lines'. A white 'diamond' square results from the space between the 4 triangles.

A rotating design, based on drawing black triangles over a drawing of grey 'construction lines'.

Another 'rotating' design, based on drawing black triangles over a drawing of grey 'construction lines'.

A design based on drawing black triangles and diamond squares over a clear white background. New shapes are formed as a result of the way that several shapes connect together.

A design based on drawing reflected black triangles and a single centre square over a clear white background.

This design is based on considering the 4 x 4 square as 4 quarters, and using the same element in each of the quarters (but rotated 90 degrees as I work my way around the quarters). This design realises one of the hand-drawn designs presented on the previous page of designs.

This design uses diagonals running between two points separated by a rise of 2 units and a width of 1 unit. This design realises one of the hand-drawn designs presented on the previous page of designs.

This is a rather complex design made up from many black triangles over a clear white background.

Again, this design is based on considering the 4 x 4 square as having 4 quarters, and using the same element in each of the quarters (but rotated 90 degrees as I work my way around the quarters).

This is another complex image, which developed from ideas I saw as I programmed other designs using Processing 3.0.

A simple growing spiral, using the smaller 8 x 8 squares.

This design uses diagonals running between two points separated by a rise of 2 units and a width of 1 unit.

This design uses diagonals running between two points separated by a rise of 2 units and a width of 1 unit.