canvas_collatz {aRtsy}

Draw Collatz Sequences

Description

This function draws the Collatz conjecture on a canvas. The conjecture of the Collatz sequence is that no matter what positive integer is chosen as the starting point of the sequence, the sequence will eventually reach the number 1. This conjecture has been verified for all starting integers up to very large numbers, but it has not been proven mathematically. Despite its simple rule, the sequence can produce long and complicated chains of numbers before eventually reaching 1. See the Details section for more specific information about the algorithm used in this function.

Usage

canvas_collatz(
  colors,
  background = "#fafafa",
  n = 200,
  angle.even = 0.0075,
  angle.odd = 0.0145,
  side = FALSE
)

Arguments

colors

a string or character vector specifying the color(s) used for the artwork.

background

a character specifying the color used for the background.

n

a positive integer specifying the number of random starting integers to use for the lines. Can also be a vector of numbers to use as starting numbers.

angle.even

a value specifying the angle (in radials) to use in bending the sequence at each odd number.

angle.odd

a value specifying the angle (in radials) to use in bending the sequence at each even number.

side

logical. Whether to put the artwork on its side.

Details

The Collatz sequence, also known as the 3n+1 problem, is a sequence of numbers generated by the following rule:

• Start with any positive integer n.

• If n is even, divide it by 2.

• If n is odd, multiply it by 3 and add 1.

• Repeat this process with the new value of n, generating a new number in the sequence.

Value

A ggplot object containing the artwork.

Author(s)

Koen Derks, [e-mail]

References

https://nl.wikipedia.org/wiki/Collatz_Conjecture

See Also

colorPalette

Examples

set.seed(1)

# Simple example
canvas_collatz(colors = colorPalette("tuscany3"))