def fernx(x,y,rand):
point=rand
if(point<=.01):
return .5
if(point<=.11):
return -.15*x+.28*y+.575
if(point<=.23):
return .2*x-.26*y+.4
return .85*x+.04*y+.075
def ferny(x,y,rand):
point=rand
if(point<=.01):
return .16*y
if(point<=.11):
return .26*x+.24*y-.086
if(point<=.23):
return .23*x+.22*y+.045
return -.04*x+.85*y+.18
array=[]
xCoordinate=1
yCoordinate=1
array.append([xCoordinate, yCoordinate])
for x in range(9):
r=random()
xO=xCoordinate
xCoordinate=fernx(xCoordinate,yCoordinate,r)
yCoordinate=ferny(xO,yCoordinate,r)
for x in range(50000):
r=random()
xO=xCoordinate
xCoordinate=fernx(xCoordinate, yCoordinate, r)
yCoordinate=ferny(xO, yCoordinate, r)
array.append([xCoordinate, yCoordinate])
show (scatter_plot(array, markersize=.004))
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def fernx(x,y,rand):
point=rand
if(point<=.01):
return .5
if(point<=.11):
return -.15*x+.18*y+.575
if(point<=.23):
return .2*x-.26*y+.4
return .85*x+.02*y+.075
def ferny(x,y,rand):
point=rand
if(point<=.01):
return .16*y
if(point<=.11):
return .26*x+.14*y-.086
if(point<=.23):
return .23*x+.18*y+.045
return -.04*x+.85*y+.18
array=[]
xCoordinate=1
yCoordinate=1
array.append([xCoordinate, yCoordinate])
for x in range(9):
r=random()
xO=xCoordinate
xCoordinate=fernx(xCoordinate,yCoordinate,r)
yCoordinate=ferny(xO,yCoordinate,r)
for x in range(50000):
r=random()
xO=xCoordinate
xCoordinate=fernx(xCoordinate, yCoordinate, r)
yCoordinate=ferny(xO, yCoordinate, r)
array.append([xCoordinate, yCoordinate])
show (scatter_plot(array, markersize=.004))
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def mandelbrotPoints(imaginary,real):
c=complex(real,imaginary)
z=complex(0,0)
for i in range(1,99):
z=(z*z)+c
if(abs(z)>2):
return i
return 0
array=[]
for j in range(100):
array.append([])
minimumReal=-1
maximumReal=.5
minimumImag=-.5
maximumImag=1
for y in range(400):
c_imaginary=minimumImag+y*(maximumImag-minimumImag)/400
for x in range(600):
c_real=minimumReal+x*(maximumReal-minimumReal)/600
m=mandelbrotPoints(c_imaginary,c_real)
if(m>0):
array[m].append([x,y])
plots=scatter_plot(array[0],markersize=.005,facecolor='green',edgecolor='blue')
for k in range(1,99):
from sage.plot.colors import green, blue
if(len(array[k])>0):
plots=plots+scatter_plot(array[k],markersize=.05,facecolor=(green.darker(fraction=10*k/100)).html_color(),edgecolor=(blue.darker(fraction=10*k/100)).html_color())
show(plots)
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def mandelbrotPoints(imaginary,real):
c=complex(real,imaginary)
z=complex(0,0)
for i in range(1,99):
z=(z*z)+c
if(abs(z)>2):
return i
return 0
array=[]
for j in range(100):
array.append([])
minimumReal=-2
maximumReal=1
minimumImag=-1.5
maximumImag=1.5
for y in range(300):
c_imaginary=minimumImag+y*(maximumImag-minimumImag)/300
for x in range(300):
c_real=minimumReal+x*(maximumReal-minimumReal)/300
m=mandelbrotPoints(c_imaginary,c_real)
if(m>0):
array[m].append([x,y])
plots=scatter_plot(array[0],markersize=.55,facecolor='orange',edgecolor='orange')
for k in range(1,99):
colors=4*k/100
from sage.plot.colors import orange
if(len(array[k])>0):
plots=plots+scatter_plot(array[k],markersize=.55,facecolor=(orange.darker(fraction=colors)).html_color(),edgecolor=(orange.darker(fraction=colors)).html_color())
show(plots)
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def midPoint(point1,point2):
return [(point1[0]+point2[0])/2,(point1[1]+point2[1])/2]
def seirpinski(t1,t2,t3,x0,iterations):
fractal=[t1,t2,t3]
points=[x0]
x=x0
for i in range(iterations):
rand=floor(3*random())
x=midPoint(fractal[rand],x)
points.append(x)
return points
s=seirpinski([0,0],[.5,.5],[1,0],[.2,.4],100000)
show(list_plot(s,size=1))
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def midPoint(point1,point2):
return [(point1[0]-point2[0])/2,(point1[1]-point2[1])/2]
def seirpinski(t1,t2,t3,t4,t5,x0,iterations):
fractal=[t1,t2,t3,t4,t5]
points=[x0]
x=x0
for i in range(iterations):
rand=floor(5*random())
x=midPoint(fractal[rand],x)
points.append(x)
return points
s=seirpinski([0,0],[.5,.5],[1,0],[.5,.5],[.5,.5],[.2,.4],500000)
show(list_plot(s,size=1))
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def midPoint(point1,point2):
return [(point1[0]-point2[0])/2,(point1[1]-point2[1])/2]
def seirpinski(t1,t2,t3,x0,iterations):
fractal=[t1,t2,t3]
points=[x0]
x=x0
for i in range(iterations):
rand=floor(3*random())
x=midPoint(fractal[rand],x)
points.append(x)
return points
s=seirpinski([0,0],[.5,.5],[1,0],[.2,.4],100000)
show(list_plot(s,size=1))
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