drawLsys {LindenmayeR}

Draw a 2D L-System Using Turtle Graphics

Description

This function takes input strings, previously created with Lsys, translates them into 2D turtle graphics instructions, and then plots the results.

Usage

drawLsys(string = NULL, drules = NULL, st = c(5, 50, 0), stepSize = 1,
  ang = 90, which = length(string), shrinkFactor = NULL, ...)

Arguments

string

A character vector giving the strings containing the turtle graphics instructions. Created by Lsys. The "language" and character set of this string is arbitary. Compare the examples below for the modified Koch curve and the Sierpinski triangle.

drules

A data frame containing columns "symbols" and "action". These contain the input symbols and the corresponding drawing action. The symbol column is in the character set used by Lsys and is arbitary. The action column entries must be from the set c("F", "f", "+", "-", "[", "]"). These are the final drawing instructions and are interpreted as follows:

"F"

Move forward drawing as you go.

"f"

Move forward w/o drawing.

"+"

Turn by positive ang.

"-"

Turn by negative ang.

"["

Save current position and heading.

"]"

Restore saved position and heading (allows one to go back).

See the examples. Note that the "action" entry always uses these symbols, though not all of them need be used.

st

A numeric vector of length 3 giving the screen coordinates where the start of the curve should be placed. The screen is 100 x 100 with the lower left corner as 0,0. The third element is the initial drawing angle in degrees.

stepSize

Numeric. The length of the drawing step.

ang

Numeric. The angle in degrees when a change in direction is requested.

which

Integer. The entries in string which should be drawn. Defaults to the last (most complex) entry. If length(which) > 1 each plot is drawn in its own window.

shrinkFactor

A numeric vector of the same length as string. As each plot is made, stepSize will be divided by the corresponding value in shrinkFactor. This allows one to scale down the increasingly large/complex plots to make them occupy a space similar to the less complex plots.

...

Additional parameters to be passed to the grid drawing routines. Most likely, something of the form gp = gpar(...). See gpar and the last example.

Value

None; side effect is a plot.

Warning

Remember that if retAll = TRUE, Lsys returns the initial string plus the results of all iterations. In this case, if you want the 5th iteration, you should specify which = 6 since the initial string is in string[1].

Examples

require('grid')

# Modified Koch curve
rkoch1 <- data.frame(inp = c("F"), out = c("F+F-F-F+F"), stringsAsFactors = FALSE)
k1 <- Lsys(init = "F", rules = rkoch1, n = 3)
dkoch <- data.frame(symbol = c("F", "f", "+", "-", "[", "]"),
action = c("F", "f", "+", "-", "[", "]"), stringsAsFactors = FALSE)
drawLsys(string = k1, stepSize = 3, st = c(10, 50, 0), drules = dkoch)
grid.text("Modified Koch Curve (n = 3)", 0.5, 0.25)

# Classic Koch snowflake
rkoch2 <- data.frame(inp = c("F"), out = c("F-F++F-F"), stringsAsFactors = FALSE)
k2 <- Lsys(init = "F++F++F", rules = rkoch2, n = 4)
drawLsys(string = k2, stepSize = 1, ang = 60, st = c(10, 25, 0), drules = dkoch)
grid.text("Classic Koch Snowflake (n = 4)", 0.5, 0.5)

# Sierpinski Triangle
rSierp <- data.frame(inp = c("A", "B"), out = c("B-A-B", "A+B+A"), stringsAsFactors = FALSE)
s <- Lsys(init = "A", rules = rSierp, n = 6)
dSierp <- data.frame(symbol = c("A", "B", "+", "-", "[", "]"),
action = c("F", "F", "+", "-", "[", "]"), stringsAsFactors = FALSE)
drawLsys(string = s, stepSize = 1, ang = 60, st = c(20, 25, 0), drules = dSierp)
grid.text("Sierpinski Triangle (n = 6)", 0.5, 0.1)

# Islands & Lakes
islands_rules <- data.frame(inp = c("F", "f"), out = c("F+f-FF+F+FF+Ff+FF-f+FF-F-FF-Ff-FFF",
"ffffff"), stringsAsFactors = FALSE)
islands <- Lsys(init = "F+F+F+F", rules = islands_rules, n = 2)
draw_islands <- data.frame(symbol = c("F", "f", "+", "-", "[", "]"),
action = c("F", "f", "+", "-", "[", "]"), stringsAsFactors = FALSE)
drawLsys(string = islands, step = 1, ang = 90, st = c(70, 35, 90),
drules = draw_islands,  gp = gpar(col = "red", fill = "gray"))

# A primitive tree (aka Pythagoras Tree)
prim_rules <- data.frame(inp = c("0", "1"),
out = c("1[+0]-0", "11"), stringsAsFactors = FALSE)
primitive_plant <- Lsys(init = "0", rules = prim_rules, n = 7)
draw_prim <- data.frame(symbol = c("0", "1", "+", "-", "[", "]"),
action = c("F", "F", "+", "-", "[", "]"), stringsAsFactors = FALSE)
drawLsys(string = primitive_plant, stepSize = 1, ang = 45, st = c(50, 5, 90),
drules = draw_prim, which = 7)
grid.text("Primitive Tree (n = 6)", 0.5, 0.75)

# A more realistic botanical structure
# Some call this a fractal tree, I think it is more like seaweed
# Try drawing the last iteration (too slow for here, but looks great)
fractal_tree_rules <- data.frame(inp = c("X", "F"),
out = c("F-[[X]+X]+F[+FX]-X", "FF"), stringsAsFactors = FALSE)
fractal_tree <- Lsys(init = "X", rules = fractal_tree_rules, n = 7)
draw_ft <- data.frame(symbol = c("X", "F", "+", "-", "[", "]"),
action = c("f", "F", "+", "-", "[", "]"), stringsAsFactors = FALSE)
drawLsys(string = fractal_tree, stepSize = 2, ang = 25, st = c(50, 5, 90),
drules = draw_ft, which = 5, gp = gpar(col = "chocolate4", fill = "honeydew"))
grid.text("Fractal Seaweed (n = 4)", 0.25, 0.25)