Um algoritmo simples é iniciar com uma haste vertical e patir dela gerar novos dois ramos:
E assim por diante:
Depois de muitas recursões, chegamos a
Podemos também tornar o processo estocástico e o surgimente de cada novo ramo depender de uma probabilidade fixa:
Eu fiz esse código para gerar as figuras acima (onde você pode brincar com os parâmetros):
import matplotlib.pyplot as plt
import math
import numpy as np
fig=plt.figure()
plt.hold(True)
plt.axis([-150, 150, -100, 300])
global cont
cont=0
np.random.seed(seed=10)
def eval_rotation_matrix(rotationAngle):
rotM11=math.cos(rotationAngle)
rotM12=-math.sin(rotationAngle)
rotM21=math.sin(rotationAngle)
rotM22=math.cos(rotationAngle)
return rotM11,rotM12,rotM21,rotM22
def image_rotation(x,y,angle):
rotM11,rotM12,rotM21,rotM22=eval_rotation_matrix(angle)
x,y=x*rotM11+y*rotM12,x*rotM21+y*rotM22
return x,y
def draw_trees(xIni,yIni,xEnd,yEnd,length,baseSize=1.0,factorSize=1.2,angle=math.pi/12,randomDraw=0.75):
global cont
if(length<baseSize):
pass
else:
cont=cont+1
print "cont",cont
if(xEnd!=xIni):
theta=math.atan((yEnd-yIni)/(xEnd-xIni))
else:
theta=math.pi/2
if(theta>=0):
if((yEnd>=yIni) and (xEnd>=xIni)):
pass
else:
theta=theta+math.pi
if(theta<0):
if((yEnd<yIni) and (xEnd>=xIni)):
pass
else:
theta=theta+math.pi
x=length
y=0
if(np.random.uniform()<randomDraw):
newX1,newY1=image_rotation(x,y,angle)
newX1,newY1=image_rotation(newX1,newY1,theta)
newX1,newY1=newX1+xEnd,newY1+yEnd
plt.plot([xEnd,newX1],[yEnd,newY1],'b')
draw_trees(xEnd,yEnd,newX1,newY1,length/factorSize)
if(np.random.uniform()<randomDraw):
newX2,newY2=image_rotation(x,y,-angle)
newX2,newY2=image_rotation(newX2,newY2,theta)
newX2,newY2=newX2+xEnd,newY2+yEnd
plt.plot([xEnd,newX2],[yEnd,newY2],'b')
draw_trees(xEnd,yEnd,newX2,newY2,length/factorSize)
if __name__ == '__main__':
# Example of Dictionary
initialSize=64.0
xIni=0
yIni=0
xEnd=xIni
yEnd=yIni+initialSize
plt.plot([xIni,xEnd],[yIni,yEnd],'b')
initialpoint=[xEnd,yEnd]
draw_trees(xIni,yIni,xEnd,yEnd,initialSize/2.0)
plt.savefig("treeStochast.png")
Uma outra possibilidade, é fazer a probabilidade de um novo ramo surgir dependendo da geração que ele pertence. Quanto maior a geração, menor a chance:
Nesse caso, eu usei esse código que é uma variação do código original:
import matplotlib.pyplot as plt
import math
import numpy as np
fig=plt.figure()
plt.hold(True)
plt.axis([-150, 150, -100, 300])
global cont
cont=0
np.random.seed(seed=10)
def eval_rotation_matrix(rotationAngle):
rotM11=math.cos(rotationAngle)
rotM12=-math.sin(rotationAngle)
rotM21=math.sin(rotationAngle)
rotM22=math.cos(rotationAngle)
return rotM11,rotM12,rotM21,rotM22
def image_rotation(x,y,angle):
rotM11,rotM12,rotM21,rotM22=eval_rotation_matrix(angle)
x,y=x*rotM11+y*rotM12,x*rotM21+y*rotM22
return x,y
def draw_trees(xIni,yIni,xEnd,yEnd,length,generation,baseSize=1/8.0,factorSize=1.2,angle=math.pi/12):
global cont
if(length<baseSize):
pass
else:
cont=cont+1
print "cont",cont
if(xEnd!=xIni):
theta=math.atan((yEnd-yIni)/(xEnd-xIni))
else:
theta=math.pi/2
if(theta>=0):
if((yEnd>=yIni) and (xEnd>=xIni)):
pass
else:
theta=theta+math.pi
if(theta<0):
if((yEnd<yIni) and (xEnd>=xIni)):
pass
else:
theta=theta+math.pi
x=length
y=0
parameter=0.05
if(np.random.uniform()<1.0/(1+parameter*generation)):
newX1,newY1=image_rotation(x,y,angle)
newX1,newY1=image_rotation(newX1,newY1,theta)
newX1,newY1=newX1+xEnd,newY1+yEnd
plt.plot([xEnd,newX1],[yEnd,newY1],'b')
draw_trees(xEnd,yEnd,newX1,newY1,length/factorSize,generation+1)
if(np.random.uniform()<1.0/(1+parameter*generation)):
newX2,newY2=image_rotation(x,y,-angle)
newX2,newY2=image_rotation(newX2,newY2,theta)
newX2,newY2=newX2+xEnd,newY2+yEnd
plt.plot([xEnd,newX2],[yEnd,newY2],'b')
draw_trees(xEnd,yEnd,newX2,newY2,length/factorSize,generation+1)
if __name__ == '__main__':
# Example of Dictionary
initialSize=64.0
xIni=0
yIni=0
xEnd=xIni
yEnd=yIni+initialSize
plt.plot([xIni,xEnd],[yIni,yEnd],'b')
initialpoint=[xEnd,yEnd]
draw_trees(xIni,yIni,xEnd,yEnd,initialSize/2.0,0)
plt.savefig("treeStochastGeneration.png")