Level 3 Coarse Holder Exponents

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

 

1. The coarse Holder exponents alpha in the level 3 table above were calculated from the level 3 probabilities using the formula alpha = Log(probability)/Log(0.125). Fill in the empty cells using the level 3 probabilities.
2. Shade the set of cell(s) with the largest coarse Holder exponent. What is the Holder exponent of the set of these cells?
3. Shade the set of cell(s) with the smallest coarse Holder exponent. What is the Holder exponent of the set of these cells?
4. What can be said about the coarse Holder exponents arranged from largest to smallest? Is there a pattern? How does this compare with the probabilities?
5. Find and shade another set whose cells all have the same coarse Holder exponent and the dimension of the set is easy to find. What is the dimension of this set?

Here are the answers.

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