Level 3 Coarse Dimensions - Answers

1. Missing values are filled in red.

2.0  
1.911  
   
1.911  
   
1.825  
   
1.911  
   
1.825  
   
1.825  
   
1.737  
   
2.107  
   
2.0  
2.020  
   
1.911  
   
2.020  
   
1.911  
   
1.932  
   
1.825  
   
2.107  
   
2.020  
   
2.0  
1.911  
   
2.020  
   
1.932  
   
1.911  
   
1.825  
   
2.215  
   
2.107  
   
2.107  
   
2.0  
2.127  
   
2.020  
   
2.020  
   
1.911  
   
2.107  
   
2.020  
   
2.020  
   
1.932  
   
2.0  
1.911  
   
1.911  
   
1.825  
   
2.215  
   
2.107  
   
2.127  
   
2.020  
   
2.107  
   
2.0  
2.020  
   
1.911  
   
2.215  
   
2.217  
   
2.107  
   
2.020  
   
2.107  
   
2.020  
   
2.0  
1.911  
   
2.322  
   
2.215  
   
2.215  
   
2.107  
   
2.215  
   
2.107  
   
2.107  
   
2.0  

 

2. The largest coarse Holder exponent occurs in the cell with address 111. Continuing this process to longer and longer addresses, this set approaches a single point, of dimension 0.
 
3. The smallest coarse Holder exponent occurs in the cell with address 444. Continuing this process to longer and longer addresses, this set approaches a single point, of dimension 0.
 
4. Recall that the higher the probability, the lower the coarse Holder exponent. Consequently, in each square, the upper right corner has the lowest coarse Holder exponent, and the lower left has the highest. This is the opposite of the corresponding relation for probabilities.
 
5. The set of cells with coarse Holder exponent 2 forms a straight line in the limit of longer and longer addresses. This set has dimension 1.

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