Booth Id:
MATH028
Category:
Mathematics
Year:
2021
Finalist Names:
Lugaro, Hector (School: CROEM HS)
Abstract:
The Collatz Conjecture and another of similar structure revolving
around congruence modulus 3, can be represented as fractals when they
are written as holomorphic functions. However, the methods to produce
these functions are increasingly complicated when working with greater
congruences, especially the indicator functions which allow the operations
to be performed to be identi fied. This research concentrates in automizing
the process of creating Collatz-type problems using computer code. The
problem was if this complicated process can be automated using computer
code. The power of 2 functions were identical after distribution, and while
the functions for the odd numbers were similar in structure, the indicator
functions were created using approximations of sine functions and square
roots. The code, apart from generating the function used to generate the
fractal, can also generate information related to the fractal including the
problem itself and a test for numbers 1 through 100. This means that the
Collatz-type problems studied in my past research, and a theoretically
infi nite range of fractals can be generated with this code, accepting my
hypothesis.