n = 4+8
"I would like %i shrubberies" % n

"'n' declared above has a value of %i" % n

import numpy
%timeit numpy.sqrt(numpy.ones((400, 400)))

values = numpy.arange(30)**2
plot(values)

import numpy
t1 = numpy.linspace(0,1,5).reshape((1, 5))
t2 = numpy.linspace(1,3,3).reshape((3, 1))
print(t1)
print(t2)
t1 + t2*1j


m = 600 # Height of plot
n = 600 # Width of plot
values_real = numpy.linspace(-2.3, 1, n).reshape((1,n))
values_imag = numpy.linspace(-1.4, 1.4, m).reshape((m,1))
initial_values = values_real + values_imag*1j
initial_values

values = initial_values
max_iterations = 30
iterations = numpy.ones(initial_values.shape) * max_iterations
for i in range(max_iterations) :
    values = values**2 + initial_values
    divergent = values * conj(values) > 4
    divergent = divergent & (iterations == max_iterations) # Test that we haven't already found this number
    iterations[divergent] = i
imshow(iterations)

rcParams['figure.figsize'] = 10, 10
imshow(iterations)

def mandelbrot(width, height, x_lim = (-2.3, 1), y_lim = (-1.4, 1.4), max_iterations = 30) :
    m = height # Height of plot
    n = width # Width of plot
    values_real = numpy.linspace(x_lim[0], x_lim[1], n).reshape((1,n))
    values_imag = numpy.linspace(y_lim[0], y_lim[1], m).reshape((m,1))
    initial_values = values_real + values_imag*1j
    initial_values
    values = initial_values
    iterations = numpy.ones(initial_values.shape) * max_iterations
    for i in range(max_iterations) :
        values = values**2 + initial_values
        divergent = values * conj(values) > 4
        divergent = divergent & (iterations == max_iterations) # Test that we haven't already found this number
        iterations[divergent] = i
    return iterations

mandelbrot_data = mandelbrot(600, 600, (-0.56, -0.55), (-0.56,-0.55), 90)
imshow(mandelbrot_data)

import pandas, ggplot
# Let's pick out a few lines from the image
mandelbrot_df = pandas.DataFrame({ i : f for i,f in enumerate(mandelbrot_data) })
mandelbrot_df

select_rows_df = pandas.melt(mandelbrot_df[[100,200,300,400]], var_name="line", value_name="iteration") # picking out row 100, 200, 300 and 400 for inspection
select_rows_df

from ggplot import *
ggplot(select_rows_df, aes(x="iteration")) + geom_histogram(binwidth = 5)

ggplot(select_rows_df, aes(x="iteration", color="line", fill="line")) + geom_density(alpha=0.3)

accumulated_rows_df = mandelbrot_df.mean().reset_index()
accumulated_rows_df

ggplot(accumulated_rows_df, aes(x="index", y=0)) + geom_line(position="jitter")