A couple weeks ago a visitor contacted me about places where she could see my maps printed out. After finding that she ived here in DC, I invited her & her husband over to look at some of the maps I have in my house. After viewing the lot, they really liked the one I made of Park City, Utah and asked if I would make one of their house that looked similar. This is the first draft. I will post the subsequent drafts as they are made….
The development of the tile I used to for this draft is actually something akin to an advancement in my own artistic endeavors. I originally made two tiles to be used- one that featured a diamond and the other featured a 16 sided polygon. I ended up using the 16-sided polygon to surround the house because it looked similar to the centers of the maps I’ve created using the Octagon Quilt Projection. The advancement I speak of is that by using an 16 sided polygon shape and having octagonal symmetry, I, for the first time, have created a unique geometric illusion.
In the Park City map I used a hexagon to outline the house and as one moves their eyes around the map they can see the hexagon rotates in conjunction with the symmetry used in the map. The illusion is that the houses rotate inside of the polygon but the polygon itself does not!
For example, along 45 degree line of symmetry, a hexagon or diamond would be rotated 45 degrees (while still being a hexagon or diamond in shape), however, in this map the polygon does not rotate because the polygon has exactly twice the number of lines of symmetry being employed in the map. Only upon closer inspection can one see that the contents of the polygon rotate along the lines of symmetry, while the polygon itself does not.