🚀 go-pugleaf

Since everyone is putting in their $0.02 worth, here is 
my penny's worth. 

Even crude estimates with the distance estimator give better upper 
   bounds than the Ewing paper. The power series converges extremely
   slowly, as can be seen by drawing the image of the unit circle by 
   the partial sum. 

Estimating the area of the interior doesn't account for the area
   of the boundary, though it is a reasonable way to get a lower bound. 
   The components of the interior are bounded by algebraic curves of 
   progressively higher order, which will be hard to compute 
   symbolically.  There is no "rescaling" or some such thing
   possible,  since M is not self similar.

Pixel counting is a waste of time, since it doesn't tell you anything
   about the area. It is not even clear that the limit of counting pixels
   at progressively high resolutions will tend to the area. (Think of 
   the "staircase" problem: Make steps of width w. As w -> 0, the steps 
   converge to a diagonal line, but the length of the steps doesn't 
   converge to the length of the line). 


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Yuval Fisher                                 e-mail: yfisher@ucsd.edu
Institute for Non-Linear Science 0402                               
University of California, San Diego                                  
La Jolla, CA 92093                                                  
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