The plants images/geometry (no mesh) are generated using L-systems from [1]. For simplicity, we do not consider the stochastic and context sensitive L-systems. We do not generate high-resolution flowers, leaves, and so on, but only generate trees.

• $V$, alphabet

• $w\in V^+$, axiom

• ${p_1, p_2, ...}$, where $p_i=(a, \chi)\in(V, V^*)$, A set of production rules

• $n$, #iterations

  From my understanding, the L-system is very similar to the Context Free Grammar (CFG), where we have

  • $V$, alphabet -> all non-terminals
  • $w\in V$, a start symbol -> non-terminal
  • ${p_1, p_2, ...}$, where $p_i=(a, \chi)\in(V, V^*)$, A set of production rules
    • To align with the definition of L-system, I finetuned the definition by removing the terminals, but make the right side of the production rule to be $V^*$ instead of $V^+$

  except that, in the L-system

  • The axiom can have multiple symbols
  • In each iteration, we must replace all the symbols using all the productions at the same time.
    • The L-system is parallel, thus representing the growth.
    • The Context Free Grammar is linear, which makes it more flexible

• General

  • $l$, step size
  • $F$ (and $F_l, F_r$), move towards $H$ for a distance of $l$
  • $f$, move towards $H$ for a distance of $l$ without drawing a line
  • $[$, start branching, push current node to stack
  • $]$, end branching, pop last node from stack
  • {, start outlining a leaf
  • }, end outlining a leaf
  • $'$, increase the current index of color
  • $A, B, C, ...$, do nothing

• 2-Dimension

  • $H=(H_x, H_y)$, turtle heading direction
  • $P=(P_x, P_y)$, turtle 2D position
  • $\delta=\alpha$:
    • $+$, turn $H$ towards left for $\alpha$ degree
    • $-$, ... right ...

  • Sample 2D non-parametric trees outputs

    Parameters refer to Figure 1.24 in Sec 1.6.3 Bracketed OL-systems (p.25) in [1].

(a)	(b)	(c)
(d)	(e)	(f)

• 3-Dimension

  • $H=(H_x, H_y, H_z)$, turtle heading direction
  • $L=(L_x, L_y, L_z)$, turtle left direction
  • $U=(U_x, U_y, U_z)$, turtle up direction
  • $P=(P_x, P_y, P_z)$, turtle 3D position
  • $\delta=\alpha$: (right-hand rule)
    • $+$, rotate around $U$ towards left for $\alpha$ degree
    • $-$, ... right ...
    • &