Random Polygons

Why random  polygons? 

3 5-sided polygon thumbnail 3 nonagon3 Many sided polygon drawn in Andes6 eleven-sided figure8 many sided polygon


Examples  Non examples  
Smooth is nice  

What's difficult about this?
  1. Connect random points on a circle
  2. Choose angles, then distances
  3. Traveling  Salesman
  4. Stitching stars
    1. two stars
    2. multiple stars
  5. Onions
Fractal surfaces:
  1. Choose any point then find a line
    1. However
  2. Choose any segment, then choose a point visible to both endpoints
Examples

Sources
[1] http://upload.wikimedia.org/wikipedia/commons/0/01/Pentagon_satellite_image.jpg
[2] http://commons.wikimedia.org/wiki/File:Eiffel_tower_2007.JPG
[3] http://maps.google.com/
[4] http://science.ksc.nasa.gov/mars/mgs/target/pio.gif
[5] http://en.wikipedia.org/wiki/File:Nazca-lineas-perro-c01.jpg