Images that show a visual representation of Fermat numbers and how those images can be used to create tessellations and other types of mathematical art.
The images are a combination of visual geometry and visual number theory with an art component.
The images are based on square grids.
The starting point for the Fermat numbers (3,5,17,257...) is a 3x3 square grid.
| 3x3 square grid |
This square grid has 4 crossing points in the center.
A new square is drawn inside of the 3x3 square grid. Parallel lines to the new square are drawn that pass through the 4 crossing middle points mentioned before. We now have a 5x5 square grid inside of the original 3x3 square grid.
| 3x3 and 5x5 square grid |
The new 5x5 square grid has now 16 crossing points inside the square.
Following the same process as before:
Draw a new square inside the 5x5 square grid, add parallel lines to the new square that pass through the crossing points and we now have a 17x17 square grid with 256 crossing points inside.
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| 3x3 grid and filling of the plane |
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| 5x5 grid and filling of the plane |
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| Tessellation |
