This GitHub repo is meant to showcase the intriguing nature of mathematical concepts such as the Kaprekar constant and Collatz conjecture. My goal is to demonstrate the captivating aspects of these mathematical phenomena.
Kaprekar constant, or 6174, is a constant that arises when we take a 4-digit integer, form the largest and smallest numbers from its digits, and then subtract these two numbers. Continuing with this process of forming and subtracting, we will always arrive at the number 6174.
Kaperkar Examples
Example of value 1237
Plot showing Kaperkar number of iterations from 1237 to 1337
The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integers in which each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that these sequences always reach 1, no matter which positive integer is chosen to start the sequence.
Collatz Conjecture Examples
Example of value 27
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. The Tinkerbell map is a two-dimensional discrete dynamical system that exhibits chaotic behavior. It is named after its resemblance to the shape of the Tinker Bell fairy from Disney's Peter Pan. The Tinkerbell map is defined by a set of iterative equations that determine the evolution of points in its phase space.
Tinkerbell Map
Example of 10,000 data points plotted
