Iterated Functions Systems Music

1991 ◽  
Vol 15 (1) ◽  
pp. 40 ◽  
Author(s):  
Michael Gogins
Keyword(s):  
Iterated Functions Systems ◽  
Iterated Functions

A HYBRID ALGORITHM FOR THE SOLUTION OF THE INVERSE PROBLEM IN FRACTAL INTERPOLATION

Fractals ◽  
2005 ◽  
Vol 13 (03) ◽  
pp. 215-226 ◽  
Author(s):  
RALPH BRINKS
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Hybrid Algorithm ◽  
High Accuracy ◽  
The Self ◽  
Fractal Interpolation ◽  
Iterated Functions Systems ◽  
Iterated Functions ◽  
Least Squares Approach

A new algorithm for the solution of the inverse problem concerning interpolatory iterated functions systems (IFS) is presented. It combines the advantages of the greedy least squares approach of Mazel and Hayes, and the self-affinity in the wavelet scalogram. Thus, the algorithm is computationally cheap and yields results with high accuracy.

scholarly journals Period Lengths for Iterated Functions

2010 ◽  
Vol 20 (2) ◽  
pp. 289-298 ◽  
Author(s):  
ERIC SCHMUTZ
Keyword(s):  
Expected Value ◽  
Iterated Functions ◽  
Image Position ◽  
Element Set

Let Ωnbe thenn-element set consisting of all functions that have {1, 2, 3, . . .,n} as both domain and codomain. LetT(f) be the order off,i.e., the period of the sequencef,f(2),f(3),f(4). . . of compositional iterates. A closely related number,B(f) = the product of the lengths of the cycles off, has previously been used as an approximation forT. This paper proves that the average values of these two quantities are quite different. The expected value ofTiswherek0is a complicated but explicitly defined constant that is approximately 3.36. The expected value ofBis much larger:

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