Build your own cycle
Choose how the numbers behave. The math handles the rest.
Choose how the numbers behave. The math handles the rest.
This site constructs sequences where an Ax + b operation alternates with a set of steps you define. You choose the multiplier A and what happens between each Ax + b. We calculate the value of b and the starting number automatically, so the sequence is guaranteed to return to where it began.
Collatz follows the classic structure: after each Ax + b, divide by 2 until you reach an odd number. You choose how many times that division happens between each step. Freestyle allows you to multiply and then divide by any non-zero integer you wish after each Ax + b step.
The standard generator supports integer variables and produces integer cycles. Irrational & Complex supports a multiplier of the form x + y√z and the resulting cycle will also include irrational and/or complex numbers. Set z to a negative value to work with complex numbers.
Purple rows are the start and end of the cycle. Orange rows are numbers fed into the Ax + b operation. Hover any truncated number to see its full value.