Generate a string art path from a rational decimal expansion

stdecimal() places digit pegs on a circle and connects consecutive digits in the expansion of a rational number. By default, the function uses base 10, so the pegs are labeled from 0 to 9.

Usage

stdecimal(
  numerator = 1,
  denominator = 7,
  n = 10,
  k = 2,
  col = "blue",
  lwd = 1,
  plot = TRUE,
  show_points = TRUE,
  show_labels = TRUE,
  verbose = FALSE,
  radius = 1,
  rotate = pi/2,
  include_integer_part = TRUE,
  show_strings = TRUE,
  template = FALSE,
  point_col = "black",
  point_cex = 0.9,
  point_pch = 21,
  point_bg = "white",
  label_cex = 0.8,
  label_col = "black",
  border_col = "grey50",
  border_lwd = 1,
  bg = "white",
  main = NULL
)

Arguments

numerator: Integer. Numerator of the rational number.
denominator: Integer. Denominator of the rational number. Must be nonzero.
n: Integer. Numeral base and number of digit pegs. Default is 10.
k: Integer. Number of repetitions of the repetend shown in the plot when the expansion is repeating. Must be at least 1.
col: String color passed to graphics::segments().
lwd: Positive number. Line width used to draw the digit path.
plot: Logical. If TRUE, draws the figure.
show_points: Logical. If TRUE, draws the digit pegs.
show_labels: Logical. If TRUE, draws digit labels.
verbose: Logical. If TRUE, prints a short audit to the console.
radius: Positive number. Circle radius.
rotate: Numeric. Rotation angle in radians applied to the digit circle.
include_integer_part: Logical. If TRUE, includes the integer part of the rational number in the displayed digit sequence.
show_strings: Logical. If TRUE, draws the digit connections.
template: Logical. If TRUE, draws only the digit template, without connections. This is equivalent to setting show_strings = FALSE and show_points = TRUE.
point_col: Peg color.
point_cex: Positive number. Peg size.
point_pch: Plotting symbol used for pegs.
point_bg: Peg background color when applicable.
label_cex: Positive number. Label size.
label_col: Label color.
border_col: Border color of the digit circle.
border_lwd: Positive number. Border line width.
bg: Plot background color.
main: Optional plot title. If NULL, no title is displayed.

Value

Invisibly returns a list of class stringart_result with:

pegs: A data.frame with columns index, x, y, and digit.
connections: A data.frame with columns connection_index, from, to, x_from, y_from, x_to, y_to, length, digit_from, digit_to, and position.
total_length: Total string length.
audit: A character vector with audit information.
meta: A list with construction metadata.

Details

The function computes the base-n expansion of numerator / denominator using exact long division. When the expansion is repeating, the repetend is displayed k times after the preperiod.

For the default setting n = 10, the function is especially useful for exploring decimal expansions, repeating decimals, periodicity, and patterns in rational numbers.

Examples

stdecimal()

stdecimal(1, 7)
stdecimal(1, 13)

stdecimal(22, 7)

stdecimal(template = TRUE)