In [1]:

    

%matplotlib notebook

import matplotlib.pyplot as plt
import numpy as np

from __future__ import print_function
from ipywidgets import interact, interactive, fixed
import ipywidgets as widgets

def plotSequence(y):
    n = np.linspace(0, y.size, y.size)
    plt.scatter(n, y)
    plt.plot([n, n], [np.zeros(n.size), y], color='gray', linestyle="--")
    return


    

In [2]:

    

def fibonacci(n):
    if n == 0:   # first initial condition
        return 0
    elif n == 1: # second initial condition
        return 1
    else:
        return fibonacci(n-1) + fibonacci(n-2)
    
   
N = 20
z = np.linspace(0,N,N)
for i in range(N):
    z[i] = fibonacci(i)

plt.figure()
plotSequence(z)


    

In [3]:

    

def fibonacciC1(n):
    return (1/np.sqrt(5))*pow(((1+np.sqrt(5))/2),n)

def fibonacciC2(n):
    return -1*(1/np.sqrt(5))*pow(((1-np.sqrt(5))/2),n)

N = 15
x = np.linspace(0,N,N)
y = np.linspace(0,N,N)
z = np.linspace(0,N,N)
for i in range(N):
    x[i] = fibonacciC1(i)
    y[i] = fibonacciC2(i)
    z[i] = x[i] + y[i]

plt.figure()
plotSequence(x)
plt.figure()
plotSequence(y)
plt.figure()
plotSequence(z)


    

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