Generate a hexagonal flower string art pattern

sthexaflower() generates a string art pattern based on three concentric hexagonal peg circuits and one central peg. The construction is fully reproducible and returns both the peg coordinates and the connection table.

Usage

sthexaflower(
  n = 24,
  k = 5,
  col = c("black", "forestgreen", "darkorange", "deepskyblue4", "firebrick", "purple"),
  lwd = 1,
  plot = TRUE,
  show_points = TRUE,
  show_labels = FALSE,
  verbose = FALSE,
  r = 1,
  scale_mid = 0.72,
  scale_inner = 0.42,
  offset_mid = 0,
  offset_inner = 0,
  rotate = 0,
  show_strings = TRUE,
  template = FALSE,
  point_col = "black",
  point_cex = 0.8,
  point_pch = 19,
  point_bg = "white",
  label_cex = 0.7,
  label_col = "black",
  border_col = "grey50",
  border_lwd = 1,
  bg = "white",
  main = NULL
)

Arguments

n: Integer. Number of pegs in each hexagonal circuit. Must be a multiple of 6 and at least 6.
k: Integer. Step used in the local modular connection rule. Must satisfy 1 <= k <= n - 1.
col: String color passed to graphics::segments(). It may have length 1 or 6. If length 6, colors are used by sector.
lwd: Positive number. Line width used to draw the strings.
plot: Logical. If TRUE, draws the figure.
show_points: Logical. If TRUE, draws the pegs.
show_labels: Logical. If TRUE, draws peg labels.
verbose: Logical. If TRUE, prints a short audit to the console.
r: Positive number. Radius of the outer hexagonal circuit.
scale_mid: Positive number in (0, 1). Scale of the middle hexagonal circuit relative to the outer circuit.
scale_inner: Positive number in (0, scale_mid). Scale of the inner hexagonal circuit relative to the outer circuit.
offset_mid: Numeric value in [0, 1). Discrete relative offset applied to the middle circuit along the peg sequence.
offset_inner: Numeric value in [0, 1). Discrete relative offset applied to the inner circuit along the peg sequence.
rotate: Numeric. Rotation angle in radians applied to the whole figure.
show_strings: Logical. If TRUE, draws the string connections.
template: Logical. If TRUE, draws only the peg template, without string 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: Hexagonal border color.
border_lwd: Positive number. Hexagonal 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 peg coordinates and metadata.
connections: A data.frame with columns connection_index, from, to, x_from, y_from, x_to, y_to, length, block, and sector.
total_length: Total string length.
audit: A character vector with audit information.
meta: A list with construction metadata.

Details

The function builds three concentric hexagonal circuits with n pegs each and one central peg.

The peg table contains the columns index, x, y, group, layer, and local_index.

The construction uses four connection blocks:

outer_border: consecutive connections on the outer hexagon.
outer_to_middle: connections from the outer circuit to the middle circuit.
middle_to_inner: connections from the middle circuit to the inner circuit.
vertices_to_center: connections from the outer vertices to the central peg.

The local additive modular rule used in the two radial blocks is

to_local = ((from_local + k - 1) %% n) + 1.

Examples

sthexaflower()


res <- sthexaflower(plot = FALSE)
head(res$pegs)
#>   index             x     y group layer local_index
#> 1     1  6.123234e-17 1.000 outer     1           1
#> 2     2 -2.165064e-01 0.875 outer     1           2
#> 3     3 -4.330127e-01 0.750 outer     1           3
#> 4     4 -6.495191e-01 0.625 outer     1           4
#> 5     5 -8.660254e-01 0.500 outer     1           5
#> 6     6 -8.660254e-01 0.250 outer     1           6
head(res$connections)
#>   connection_index from to        x_from y_from       x_to         y_to length
#> 1                1    1  2  6.123234e-17  1.000 -0.2165064 8.750000e-01   0.25
#> 2                2    2  3 -2.165064e-01  0.875 -0.4330127 7.500000e-01   0.25
#> 3                3    3  4 -4.330127e-01  0.750 -0.6495191 6.250000e-01   0.25
#> 4                4    4  5 -6.495191e-01  0.625 -0.8660254 5.000000e-01   0.25
#> 5                5    5  6 -8.660254e-01  0.500 -0.8660254 2.500000e-01   0.25
#> 6                6    6  7 -8.660254e-01  0.250 -0.8660254 3.053113e-16   0.25
#>          block sector
#> 1 outer_border      1
#> 2 outer_border      1
#> 3 outer_border      1
#> 4 outer_border      1
#> 5 outer_border      2
#> 6 outer_border      2
res$total_length
#> [1] 51.73785

sthexaflower(n = 30, k = 7, col = "steelblue", lwd = 0.8)

sthexaflower(n = 24, k = 5, show_points = TRUE, show_labels = TRUE)

sthexaflower(template = TRUE)