# Draw a 2D L-System Using Turtle Graphics This function takes input strings, previously created with `Lsys`, translates them into 2D turtle graphics instructions, and then plots the results. ```r 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. ## Returns 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 ```r 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) ```

drawLsys function