sierpinski_maze {mazealls}

sierpinski_maze .

Description

Recursively draw a Sierpinski triangle maze. The sides of the triangle consist of 2^{depth} pieces of length unit_len. The ‘inner’ and ‘outer’ pieces of the flake are mazes drawn in different colors.

Usage

sierpinski_maze(depth, unit_len, clockwise = TRUE,
  start_from = c("midpoint", "corner"), method = "random",
  style = c("four_triangles", "hexaflake", "dragon_left", "dragon_right"),
  color1 = "black", color2 = "gray40", draw_boundary = FALSE,
  num_boundary_holes = 2, boundary_lines = TRUE, boundary_holes = NULL,
  boundary_hole_color = NULL, boundary_hole_locations = NULL,
  boundary_hole_arrows = FALSE, end_side = 1)

Arguments

depth

the depth of recursion. This controls the side length. Should be an integer.

unit_len

the unit length in graph coordinates. This controls the width of the ‘holes’ in the boundary lines and generally controls the spacing of mazes.

clockwise

whether to draw clockwise.

start_from

whether to start from the midpoint of the first side of a maze, or from the corner facing the first side.

method

controls the method to draw the underlying equilateral triangles. See eq_triangle_maze.

style

controls the style of Sierpinski triangle. The following are recognized:

four_triangles

The traditional Sierpinski Triangle of four triangles with the center in the minor color, color2.

hexaflake

Looks more like a hexaflake in a triangle.

dragon_left

Looks like a dragon fractal.

dragon_right

Looks like a dragon fractal.

color1

The dominant color of the maze.

color2

The negative color of the maze.

draw_boundary

a boolean indicating whether a final boundary shall be drawn around the maze.

num_boundary_holes

the number of boundary sides which should be randomly selected to have holes. Note that the boundary_holes parameter takes precedence.

boundary_lines

indicates which of the sides of the maze shall have drawn boundary lines. Can be a logical array indicating which sides shall have lines, or a numeric array, giving the index of sides that shall have lines.

boundary_holes

an array indicating which of the boundary lines have holes. If NULL, then boundary holes are randomly selected by the num_boundary_holes parameter. If numeric, indicates which sides of the maze shall have holes. If a boolean array, indicates which of the sides shall have holes. These forms are recycled if needed. See holey_path. Note that if no line is drawn, no hole can be drawn either.

boundary_hole_color

the color of boundary holes. A value of NULL indicates no colored holes. See holey_path for more details. Can be an array of colors, or colors and the value 'clear', which stands in for NULL to indicate no filled hole to be drawn.

boundary_hole_locations

the ‘locations’ of the boundary holes within each boundary segment. A value of NULL indicates the code may randomly choose, as is the default. May be a numeric array. A positive value up to the side length is interpreted as the location to place the boundary hole. A negative value is interpreted as counting down from the side length plus 1. A value of zero corresponds to allowing the code to pick the location within a segment. A value of NA may cause an error.

boundary_hole_arrows

a boolean or boolean array indicating whether to draw perpendicular double arrows at the boundary holes, as a visual guide. These can be useful for locating the entry and exit points of a maze.

end_side

the number of the side to end on. A value of 1 corresponds to the starting side, while higher numbers correspond to the drawn side of the figure in the canonical order (that is, the order induced by the clockwise parameter).

Details

Draws a maze in an Sierpinski equilateral Triangle. The inner quarter is drawn in the secondary color, while the outer three quarters are drawn recursively. This is the traditional Sierpinski Triangle, generated when style=='four_triangles':

Value

nothing; the function is called for side effects only, though in the future this might return information about the drawn boundary of the shape.

Author(s)

Steven E. Pav [e-mail]

See Also

eq_triangle_maze, hexaflake_maze, sierpinski_carpet_maze, sierpinski_trapezoid_maze,

Examples

library(TurtleGraphics)
turtle_init(1000,1000,mode='clip')
turtle_up()
turtle_hide()
turtle_do({
	turtle_setpos(10,500)
	turtle_setangle(0)
	sierpinski_maze(depth=5,unit_len=19,boundary_lines=TRUE,
	  boundary_holes=c(1,3),color1='black',color2='gray60')
})