Recall that if all the scaling factors ri take on a common value, r, the tau(q) equation can be solved explicitly: |
tau(q) = -ln(p1q + ... + pNq)/ln(r). |
As an illustration, take these values: |
Fill in the tau(q) values for this table.
  q   |   tau(q)   |
  -2   |   |
  -1   |   |
  0   |   |
  1   |   |
  2   |   |
  5   |   |
Plot these points and sketch the tau(q) curve. Here are the completed table and the graph.
 
As another illustration take these values: |
Fill in the tau(q) values for this table.
  q   |   tau(q)   |
  -2   |   |
  -1   |   |
  0   |   |
  1   |   |
  2   |   |
  5   |   |
Plot these points and sketch the tau(q) curve. Here are the completed table and the graph.
 
From these graphs, comment on | |||||
| |||||
| |||||
| |||||
| |||||
| |||||
| |||||
| |||||
| |||||
| |||||
|
Return to Multifractals.