Alumni Keith Gross ’09 and Brendan Sullivan ’07 with Yale alumna Jennifer Lanski have published an article with Professor of Mathematics Richard Bedient and Yale Professor Michael Frame in the journal Fractals. The paper, titled “Higher Block IFS: Memory Reduction and Dimension Computations,” is the result of work over a period of years by the authors as parts of various senior projects.
Many fractals are constructed by randomly choosing one of a set of rules, applying that rule and then repeating the process infinitely. In this paper the authors examine what happens if the choosing process isn’t quite random. Imagine a die that will never roll a five immediately after it rolls a three but behaves randomly otherwise. The resulting images can be quite complex mathematically and beautiful at the same time.
Many fractals are constructed by randomly choosing one of a set of rules, applying that rule and then repeating the process infinitely. In this paper the authors examine what happens if the choosing process isn’t quite random. Imagine a die that will never roll a five immediately after it rolls a three but behaves randomly otherwise. The resulting images can be quite complex mathematically and beautiful at the same time.
