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Project: Dynamics 2019
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Kernel: SageMath 8.6
5*4
20
sin(pi/6)
1/2
f(x) = sin(x)/x^2

f(pi)
0
f(1)
sin(1)
plot(f, 1, 10)
Image in a Jupyter notebook
f(x) = 4*x*(1-x)

plot(f, 0, 1, aspect_ratio=1)
Image in a Jupyter notebook
identity(x) = x
plot(identity, 0, 1, aspect_ratio=1, color="red")
Image in a Jupyter notebook
plt = plot(f, 0, 1, aspect_ratio=1) + \
        plot(identity, 0, 1, aspect_ratio=1, color="red")
plt
Image in a Jupyter notebook
x = 1/3
y = f(x)
path = [(x,x), (x, y)]
plt + line2d(path, color="green")
Image in a Jupyter notebook
for i in range(10):
    print(i)
0 1 2 3 4 5 6 7 8 9 
x = 1/3
y = f(x)
path = [(x,x), (x, y)]
for i in range(10):
    x = y
    y = f(x)
    path.append( (x,x) )
    path.append( (x,y) )
plt + line2d(path, color="green")
Image in a Jupyter notebook
f(8/9)
32/81