text: from __future__ import annotations
  from typing import List
  import random
  
  from bonsai.structures import Command, Branch, Push, Pop, BranchKind, LSystem, BranchSnapshot
  
  
  def koch_island(d: int = 10) -> LSystem:
      FORWARD = BranchKind(1)
  
      f = Branch(angle=0, length=d, kind=FORWARD)
      tp = Branch(angle=90, length=0)
      tn = Branch(angle=-90, length=0)
  
      system = LSystem([f, tn, f, tn, f, tn, f], recommended_depth=4)
  
      @system.add_rule(FORWARD)
      def f_replace(_: BranchSnapshot) -> List[Command]:
          return [f, tn, f, tp, f, tp, f, f, tn, f, tn, f, tp, f]
  
      return system
  
  
  def dragon_curve(d: int = 10) -> LSystem:
      T1 = BranchKind(1)
      T2 = BranchKind(2)
  
      f1 = Branch(angle=0, length=d, kind=T1)
      f2 = Branch(angle=0, length=d, kind=T2)
      tp = Branch(angle=90, length=0)
      tn = Branch(angle=-90, length=0)
  
      system = LSystem([f1], recommended_depth=10)
  
      @system.add_rule(T1)
      def f1_replace(_: BranchSnapshot) -> List[Command]:
          return [f1, tp, f2, tp]
  
      @system.add_rule(T2)
      def f2_replace(_: BranchSnapshot) -> List[Command]:
          return [tn, f1, tn, f2]
  
      return system
  
  
  def bushy_tree(d: int = 10) -> LSystem:
      FORWARD = BranchKind(1)
  
      f = Branch(angle=0, length=d, kind=FORWARD)
      tp = Branch(angle=22.5, length=0)
      tn = Branch(angle=-22.5, length=0)
      push = Push()
      pop = Pop()
  
      system = LSystem([f], recommended_depth=4)
  
      @system.add_rule(FORWARD)
      def f_replace(_: BranchSnapshot) -> List[Command]:
          return [f, f, tn, push, tn, f, tp, f, tp, f, pop, tp, push, tp, f, tn, f, tn, f, pop]
  
      return system
  
  
  def flower_field(d: int = 10) -> LSystem:
      FORWARD = BranchKind(1)
  
      f = Branch(angle=0, length=d, kind=FORWARD)
      tp = Branch(angle=30, length=0)
      tn = Branch(angle=-30, length=0)
      push = Push()
      pop = Pop()
  
      system = LSystem([f], recommended_depth=4)
  
      @system.add_rule(FORWARD)
      def f_replace(_: BranchSnapshot) -> List[Command]:
          r = random.random()
          if r <= 0.33:
              return [f, push, tp, f, pop, f, push, tn, f, pop, f]
          elif r <= 0.66:
              return [f, push, tp, f, pop, f]
          else:
              return [f, push, tn, f, pop, f]
  
      return system
  
  
  def triangle_koch(d: int = 400) -> LSystem:
      c = 1
      p = 0.3
      q = c - p
      h = (p * q)**0.5
  
      FORWARD = BranchKind(1)
      tp = Branch(angle=86, length=0)
      tn = Branch(angle=-86, length=0)
      def forward(d: float) -> Branch:
          return Branch(angle=0, length=d, kind=FORWARD)
  
      system = LSystem([forward(d)], recommended_depth=4)
  
      @system.add_rule(FORWARD)
      def f_replace(snapshot: BranchSnapshot) -> List[Command]:
          x = snapshot.branch.length
          return [forward(x * p), tp, forward(x * h), tn, tn, forward(x * h), tp, forward(x * q)]
  
      return system
  
  