Plants

Blue dragonflies dart to and fro I tie my life to your balloon and let it go (Warm Foothills, Alt-J)

In my last post I did some drawings based on L-Systems. These drawings are done sequentially. At any step, the state of the drawing can be described by the position (coordinates) and the orientation of the pencil. In that case I only used two kind of operators: drawing a straight line and turning a constant angle. Today I used two more symbols to do stack operations:

• “[“ Push the current state (position and orientation) of the pencil onto a pushdown operations stack
• “]” Pop a state from the stack and make it the current state of the pencil (no line is drawn)

These operators allow to return to a previous state to continue drawing from there. Using them you can draw plants like these:

Each image corresponds to a different axiom, rules, angle and depth. I described these terms in my previous post. If you want to reproduce them you can find the code below (each image corresponds to a different set of axiom, rules, angle and depth parameters). Change colors, add noise to angles, try your own plants … I am sure you will find nice images:

library(gsubfn)library(stringr)library(dplyr)library(ggplot2)#Plant 1axiom="F"rules=list("F"="FF-[-F+F+F]+[+F-F-F]")angle=22.5depth=4#Plant 2axiom="X"rules=list("X"="F[+X][-X]FX", "F"="FF")angle=25.7depth=7#Plant 3axiom="X"rules=list("X"="F[+X]F[-X]+X", "F"="FF")angle=20depth=7#Plant 4axiom="X"rules=list("X"="F-[[X]+X]+F[+FX]-X", "F"="FF")angle=22.5depth=5#Plant 5axiom="F"rules=list("F"="F[+F]F[-F]F")angle=25.7depth=5#Plant 6axiom="F"rules=list("F"="F[+F]F[-F][F]")angle=20depth=5for (i in 1:depth) axiom=gsubfn(".", rules, axiom)actions=str_extract_all(axiom, "\\d*\\+|\\d*\\-|F|L|R|\\[|\\]|\\|") %>% unliststatus=data.frame(x=numeric(0), y=numeric(0), alfa=numeric(0))points=data.frame(x1 = 0, y1 = 0, x2 = NA, y2 = NA, alfa=90, depth=1)for (action in actions) {  if (action=="F")  {    x=points[1, "x1"]+cos(points[1, "alfa"]*(pi/180))    y=points[1, "y1"]+sin(points[1, "alfa"]*(pi/180))    points[1,"x2"]=x    points[1,"y2"]=y    data.frame(x1 = x, y1 = y, x2 = NA, y2 = NA,                alfa=points[1, "alfa"],               depth=points[1,"depth"]) %>% rbind(points)->points  }  if (action %in% c("+", "-")){    alfa=points[1, "alfa"]    points[1, "alfa"]=eval(parse(text=paste0("alfa",action, angle)))  }  if(action=="["){     data.frame(x=points[1, "x1"], y=points[1, "y1"], alfa=points[1, "alfa"]) %>%       rbind(status) -> status    points[1, "depth"]=points[1, "depth"]+1  }    if(action=="]"){     depth=points[1, "depth"]    points[-1,]->points    data.frame(x1=status[1, "x"], y1=status[1, "y"], x2=NA, y2=NA,                alfa=status[1, "alfa"],               depth=depth-1) %>%       rbind(points) -> points    status[-1,]->status  }}ggplot() +   geom_segment(aes(x = x1, y = y1, xend = x2, yend = y2),                lineend = "round",                colour="white",               data=na.omit(points)) +   coord_fixed(ratio = 1) +  theme(legend.position="none",        panel.background = element_rect(fill="black"),        panel.grid=element_blank(),        axis.ticks=element_blank(),        axis.title=element_blank(),        axis.text=element_blank())

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