Creator

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Creator can be used to create/find a family of IFS.

Yo can open creator from the main menu "File"->"New" or from the toolbar.


Usually you should:

  1. Fill "Graph" field
  2. Optionally change other parameters
  3. Press "Search" button
  4. Press "Stop" button
  5. Select group (and polynomial) from the list
  6. Press "Create" button

After it the program will switch to the IFS search mode.

When you find enough number of IFS (that can have dimension less than you are expected), you can switch to another search mode (in the "Finder" window) by:

  • setting "#var maps" field to >=1
  • decreasing "#empty maps"

Sometimes you need many hours to find something interesting, sometimes only several seconds!


Examples:


Chair tile family (or Square family):

One set: "A" that consists from 4 smaller pieces of itself with the same coefficients k

We denote graph as: a.a.a.a or 4a

Group=C4 (360/4=90 degree rotation + reflection), Poly=2


Rauzy tile family:

One set: A that consists from 3 smaller copies of itself with coefficients k,k^2,k^3

We denote graph as: a.a2.a3

Group=B2 (360/2=180 degree rotation), Poly=x^3-x^2+x+1


Robinson triangle family:

Two sets: A,B

A consists from 3 smaller copies of A,A,B with coefficient k

B consists from 2 smaller copies of A,B with coefficient k

We denote graph as: a.a.b-a.b or 2a.b-a.b

Group=C10 (360/10=36 degree rotation + reflection), Poly=-x^3+x^2+1