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Generalized
Cantor functions: random function iteration
Jordan Armstrong and Lisbeth Schaubroeck
Vol. 13 (2020), No. 2, 281–299
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Abstract |
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We provide a generalization of the classical Cantor function. One characterization of the Cantor function is generated by a sequence of real numbers that starts with a seed value and at each step randomly applies one of two different linear functions. The Cantor function is defined as the probability that this sequence approaches infinity. We generalize the Cantor function to instead use a set of any number of linear functions with integer coefficients. We completely describe the resulting probability function and give a full explanation of which intervals of seed values lead to a constant probability function value. |
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Keywords
iteration, cantor function, sequence, devil's staircase
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Mathematical Subject Classification 2010
Primary: 26A18
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Milestones
Received: 13 May 2019
Revised: 11 December 2019
Accepted: 23 December 2019
Published: 30 March 2020
Communicated by Michael Dorff
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Authors |
| Jordan Armstrong | |
| Department of Mathematical
Sciences U.S. Air Force Academy Air Force Academy, CO United States |
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| Lisbeth Schaubroeck | |
| Department of Mathematical
Sciences U.S. Air Force Academy Air Force Academy, CO United States |
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