Dargon Curve Python

The dragon curve fractal can be defined in a Lindenmayer System. The method can be easily acquire in the math websites or in wikipedia. Here is a sample:

• angle 90°
• initial string FX
• string rewriting rules
  • X ↦ X+YF+
  • Y ↦ −FX−Y 
  
   This can be describe as:
  
  • start with a base segment
  • replace each segment by 2 segment with a right angle and a rotation of 45 degrees
  
  
  Here is a further explanation 
  
  • + = turn right
  • - = turn left 
  • F = go forward 
  • FX = initial string 
  • X = X+YF+
  • Y = -FX-Y
  
  In our python we will control the generation through some inputs
  
  
  •  length, =  is the distance the turtle function will travel (the drawn line)
  •  angle, = angle of the turtles rotation
  • level, = this is the iteration level
  • first_state = this is the L-systems starting description basically FX
  •  tar1, =character to replace the each iteration
  • tar2,  = character to replace the each iteration
  • replace, = the character/value to replace with
  • replace2 = the character/value to replace with
  
  
   Here we start an initial state of FX. Remember we a rule that states that every X in the list is replace with X+YF+. We get F(X+YF+) or FX+YF+. This basically means Move Forward -> Turn Right -> Move Forward -> Turn Right. This creates a corner 
  
  In the next iteration we replace all Y characters with -FX-Y.
   our first corner was FX+YF++-FX-Y.F+
  
  Here is a value in 5 level:
  FX+YF++-FX-YF++-FX+YF+--FX-YF++-FX+YF++-FX-YF+--FX+YF+--FX-YF++-FX+YF++-FX-YF++-FX+YF+--FX-YF+--FX+YF++-FX-YF+--FX+YF+--FX-YF+
  
  Here is a piece of the code :
  # this means all the names in the turtle module will be available to us
  from turtle import *
  
  # in here we try and state the varaibles which are going to be used for our loops
  def DragonCurve(length, angle, level,first_state, tar1,replace, tar2, replace2):
  
  constant = first_state
  
  for count in range(level):
  constant2 = ''
  for char in constant:
  

  if char == tar1:
  

  constant2 +=replace

  elif char == tar2:
  

  constant2 +=replace2

  else:
  

  constant2 +=char

  constant = constant2
  
  
  # this will try and draw our dragon curve based on the value taken from previous loop
  for char in constant:
  if char =='F':
  

  forward(length)

  elif char == '+':
  

  right(angle)

  elif char =='-':
  

  left(angle)
  # this is a turtle command that takes the speed of our drawing
  speed(50)
  hideturtle()
  # this will start up our commands
  DragonCurve(10,90,10,'FX+FX+','X','X+YF','Y','FX-Y')

The Simple RIB

this is our simple renderman RIB file with our simple shader. The shader will have procedural pattern plug into it to produce the appearance of our shader and the growth of the frost. all of this will be done through python.

Our RIB FILE
    
Display "" "framebuffer" "rgba"
Format 250 250 1
Projection "perspective" "fov" 40

 
Translate  0 0 3
Rotate -30 1 0 0
Rotate 0   0 1 0
Scale 1 1 -1

WorldBegin
    LightSource "pointlight" 1 "intensity" 30 "from" [2 2 2]
    TransformBegin
        Surface "FrostBase"
        AttributeBegin
       
               
        AttributeEnd
        Color 0.078 0.120 0.160
        Sphere 1 -1 1 360
    TransformEnd
WorldEnd



Our Base Shader

surface FrostBase(float Kd = 0.8,
                   frost = 0.5)
                  
{
normal  n = normalize(N),
        nf = faceforward(n, I);
float   hump = 0;
color   surfcolor = Cs;
 

color  diffusecolor = Kd * diffuse(nf);
Oi = Os;
Ci = Oi * surfcolor * diffusecolor;
}