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 1 axiom="F" rules=list("F"="FF-[-F+F+F]+[+F-F-F]") angle=22.5 depth=4 #Plant 2 axiom="X" rules=list("X"="F[+X][-X]FX", "F"="FF") angle=25.7 depth=7 #Plant 3 axiom="X" rules=list("X"="F[+X]F[-X]+X", "F"="FF") angle=20 depth=7 #Plant 4 axiom="X" rules=list("X"="F-[[X]+X]+F[+FX]-X", "F"="FF") angle=22.5 depth=5 #Plant 5 axiom="F" rules=list("F"="F[+F]F[-F]F") angle=25.7 depth=5 #Plant 6 axiom="F" rules=list("F"="F[+F]F[-F][F]") angle=20 depth=5 for (i in 1:depth) axiom=gsubfn(".", rules, axiom) actions=str_extract_all(axiom, "\\d*\\+|\\d*\\-|F|L|R|\\[|\\]|\\|") %>% unlist status=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())

It’s so beautiful!

I’m always surprised here, thanks!

Thanks to you!!

Always amazed

Wow, it is amazing!