Lindenmayer Growth

Plants and curves grown from a string of symbols. Each level rewrites every symbol by a rule; a turtle then draws the string. Pick a rule set, then move the level.


  


  

    
    
    


    
    

    
Rules

    
    

    
    Counts
    
    
    
      
    Symbols in string
    
      
    Segments drawn
    
      
    Formula
    
      
    Lengths so far
    
    
    
  
    

    


    
  
    Notes
    
  
    The string is built in full, not by drawing. The page stops rewriting at 300,000 symbols so a level
  never freezes the tab; the level slider ends where that limit does. Drawings with no turtle meaning (Lindenmayer's
  algae) are shown as a row of tiles: A and B are the two colours.
    
  
    The formula rows are exact: the Koch segment count is 5n, the dragon's is 2n, the
  arrowhead's is 3n, and the algae string length is the Fibonacci number F(n+2). The plant has no simple
  formula, so the page shows none.