# Jos Vromans

In my work, I am exploring different concepts of mathematics. There is no better way of understanding such concepts than by implementing them yourself, visualizing them and visualizing variations of it.

I do this by writing my own software that generates images. I implement algorithms to generate a pattern or a collection of geometrical shapes. Even with basic shapes and logic, complex-looking results can be made by using the power of iteration.

After I implement one idea, I change some parameters or some logic in the code in a quest for new variations. The effect on the result is sometimes surprising and beyond my capibilities to predict. It excites me to know that there are many variations out there that I have yet to discover.

This piece is made by adding smaller squares within the previous square, starting with one large square. There are two iterations happening at once, one clockwise and one counter clockwise, which results in intersecting lines. When each next square starts at half a square root of two times the side length of the previous square, all the lines will line up perfectly. The result is a flower-like shape, and divides the original square in many triangles, getting smaller and smaller towards the center. This division of the plane is 2-colorable, which means I can iterate over every single triangle as well, with every clockwise iterating triangle neighbouring only counter-clockwise iterating ones.

The lines are partly colored in random colors.

This piece is based on the 'Root two flower' that I described for the other piece. The flower shape can still be seen, laying on the ground.

For this piece, I made the triangles bigger in every iteration so that they literally grow out of the base shape. I can choose certain parameters in such way, that the growth will be in one direction only. For this piece I found a configuration where the growth is upwards, and where the triangles near the center stay relatively small, and the triangles further from the center grow pretty big.