# Intro

This notebook explores introductory concepts and examples of generative art and computational creativity, especially guided/driven by the related Kadenze Online course.

Generative Art: art generated via automated/autonomous procedures/processes

Computational Creativity: study of autonomous/computational process/systems for the resolution of creative tasks



In :

# Basic libraries import
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
import matplotlib
from matplotlib import animation
from PIL import Image, ImageDraw

import os
import sys

import itertools
import collections

from math import cos, sin, pi

# Plotting
%matplotlib notebook

sns.set_context("paper")
sns.set_style("dark")




In :

# util method to plot multiple version of same generative artwork
def plot_artworks(artwork_gen_fun, nb_plots_side):
# Create a grid of random colours arrangement pieces
fig, axarr = plt.subplots(nb_plots_side, nb_plots_side)
for row in range(nb_plots_side):
for col in range(nb_plots_side):
axarr[row, col].imshow(artwork_gen_fun(row, col))
axarr[row, col].set_title('')
axarr[row, col].axis('off')
plt.show()



# Colours Arranged by Chance

Mimicry of Gerhard Richter’s 4900 Colours artwork.

Description: generate NxM grid of squares each assigned with a random color.

• actual logic behind choice of color schema or more specific/meaningful seeding for the stochastic process
• Mondrian imitation


In :

def generate_colours_arranged(nb_squares_side: int, square_side: int):
img_side = nb_squares_side * square_side
img = Image.new('RGB', (img_side, img_side), (255, 255, 255))

draw = ImageDraw.Draw(img)
for x in range(nb_squares_side):
for y in range(nb_squares_side):
cur_x_pos = x*square_side
cur_y_pos = y*square_side
rand_color = np.random.randint(256, size=3)
draw.rectangle([cur_x_pos, cur_y_pos,
cur_x_pos+square_side, cur_y_pos+square_side],
fill=tuple(rand_color))

return img




In :

nb_squares_side = 5
square_side = 10

plot_artworks(lambda row, col: generate_colours_arranged(nb_squares_side, square_side),
nb_plots_side=4)







In :

# test to generate something similar to Mondrian work
# here just a very rough/minimal example
def generate_mondrian(width: int, height: int):
img_side = nb_squares_side * square_side
img = Image.new('RGB', (width, height), (255, 255, 255))

g_const = 5
num_rects = g_const*g_const
rect_min_side = width/g_const
rect_max_side = rect_min_side * 2

draw = ImageDraw.Draw(img)
prev_x_pos = 0
prev_y_pos = 0
for i in range(num_rects):
rect_width = np.random.randint(rect_min_side, rect_max_side)
rect_height = np.random.randint(rect_min_side, rect_max_side)
rand_color = np.random.randint(256, size=3)
draw.rectangle([prev_x_pos, prev_y_pos,
prev_x_pos+rect_width, prev_y_pos+rect_height],
fill=tuple(rand_color),
outline=(0, 0, 0))
prev_x_pos += rect_width
if prev_x_pos > width:
prev_x_pos = 0
prev_y_pos += rect_height

return img




In :

plot_artworks(lambda row, col: generate_mondrian(width=300, height=400),
nb_plots_side=2)






# Fractals

Mathematical chaotic systems that have property of self-similarity (expanding/evolving simmetry).

3Blue1Brown on Fractals, and the fact that they are typically not self-similar

Related concepts:

• chaos theory
• attractors

## Sierpinski Triangle

• generalize by shape
• 3D version (use Blender)


In :

# draw the emergent central triangle (white) in a recursive way
# to simulate the sierpinski triangle
def rec_shrink_step(draw, triangle: list, depth: int=0, max_depth=1):
# stop condition
if depth >max_depth:
return

# for now just draw the emergent central hole
hole = [((triangle-triangle)/2+triangle, (triangle-triangle)/2+triangle),
((triangle-triangle)/2+triangle, (triangle-triangle)/2+triangle),
((triangle, triangle))]
draw.polygon(hole, fill=(255, 255, 255))
t1 = [triangle, hole, hole]
t2 = [hole, triangle, hole]
t3 = [hole, hole, triangle]
rec_shrink_step(draw, t1, depth+1, max_depth)
rec_shrink_step(draw, t2, depth+1, max_depth)
rec_shrink_step(draw, t3, depth+1, max_depth)




In :

# main method to draw a sierpinski triangle
def sierpinski_triangle(img_side: int, max_depth: int):
img = Image.new('RGB', (img_side, img_side), (255, 255, 255))

draw = ImageDraw.Draw(img)
triangle = [(0, img_side), (img_side/2, 0), (img_side, img_side)]
triangle_color = (0, 0, 0)
draw.polygon(triangle, fill=triangle_color)
rec_shrink_step(draw, triangle, max_depth=max_depth)
return img




In :

sierpinski_triangle(500, 4)




Out:




In :

plot_artworks(lambda row, col: sierpinski_triangle(1000, row+col),
nb_plots_side=4)






# L-System

L-system or Lindenmayer system is a parallel rewriting systems. Parallel because "as many rules as possible are applied simultaneously, per iteration". This differs from a formal grammar that instead applies one rule per iteration.

An L-system consist of an alphabet (variables + constants), a collection of production rules and an initial axiom. Optionally for graphic representation a translation mechanism is used to translate a string to a geometry.

L-Systems can be used to generate self-similar fractals.

Disclaimer: in some of the following examples I obtain visual results that are similar but actually wrong as I am applying the drawing rule to values before they are expanded and then proceed with the recursion.

A more correct approach would be to get the results from the final iteration and then proceed to apply the drawing rule. Turtle is probably the most suited Python library for the drawing task.

## Algae

"Lindenmayer's original L-system for modelling the growth of algae."



In :

# L-system definition
variables = ['B', 'A']
axiom = ['A']
def rules(var):
# verify that given var is in the system alphabet
if var not in variables:
raise Exception("{} not in the alphabet".format(var))
if var == 'A':
return ['A', 'B']
elif var == 'B':
return ['A']




In :

NB_ITERATIONS = 10

res = axiom
for i in range(1, NB_ITERATIONS):
res = list(itertools.chain(*[rules(x) for x in res]))
print("n = {} : {}".format(i, res))




n = 1 : ['A', 'B']
n = 2 : ['A', 'B', 'A']
n = 3 : ['A', 'B', 'A', 'A', 'B']
n = 4 : ['A', 'B', 'A', 'A', 'B', 'A', 'B', 'A']
n = 5 : ['A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B']
n = 6 : ['A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A']
n = 7 : ['A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B']
n = 8 : ['A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A']
n = 9 : ['A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B', 'A', 'B', 'A', 'A', 'B', 'A', 'A', 'B']



## Koch Curve



In :

# L-system definition
variables = ['F']
constants = ['-', '+']
axiom = ['F']
def rules(val):
# verify that given val is in the system alphabet
if val not in variables and val not in constants:
raise Exception("{} not in the alphabet".format(val))
if val in constants:
return []
elif val == 'F':
return list('F+F-F-F+F')




In :

def rec_draw_koch_curve(draw, vals, pos: tuple, angle=0, depth=0, max_depth=3):
LINE_LENGTH = 10

if depth >= max_depth:
return angle, pos

for val in vals:
if val == '+':
elif val == '-':
elif val == 'F':
new_pos =  (pos + LINE_LENGTH*cos(angle*(pi/180)),pos + LINE_LENGTH*sin(angle*(pi/180)))
draw.line([pos, new_pos], fill=(0, 0, 255))
pos = new_pos
angle, pos = rec_draw_koch_curve(draw, rules(val), pos, angle, depth=depth+1, max_depth=max_depth)
return angle, pos




In :

img = Image.new('RGB', (500, 500), (255, 255, 255))
draw = ImageDraw.Draw(img)
rec_draw_koch_curve(draw, axiom, (199, 50), 90, 0, max_depth=5)
img




Out:



## Fractal Plant



In :

# L-system definition
variables = ['X', 'F']
constants = ['-', '+', '[', ']']
axiom = ['X']
def rules(val):
# verify that given var is in the system alphabet
if val not in variables and val not in constants:
raise Exception("{} not in the alphabet".format(val))
if val in constants:
return [val]
elif val == 'X':
return list('F+[[X]-X]-F[-FX]+X')
elif val == 'F':
return ['F', 'F']




In :

NB_ITERATIONS = 3

res = axiom
for i in range(1, NB_ITERATIONS):
res = list(itertools.chain(*[rules(x) for x in res]))
print("n = {} : {}".format(i, res))




n = 1 : ['F', '+', '[', '[', 'X', ']', '-', 'X', ']', '-', 'F', '[', '-', 'F', 'X', ']', '+', 'X']
n = 2 : ['F', 'F', '+', '[', '[', 'F', '+', '[', '[', 'X', ']', '-', 'X', ']', '-', 'F', '[', '-', 'F', 'X', ']', '+', 'X', ']', '-', 'F', '+', '[', '[', 'X', ']', '-', 'X', ']', '-', 'F', '[', '-', 'F', 'X', ']', '+', 'X', ']', '-', 'F', 'F', '[', '-', 'F', 'F', 'F', '+', '[', '[', 'X', ']', '-', 'X', ']', '-', 'F', '[', '-', 'F', 'X', ']', '+', 'X', ']', '+', 'F', '+', '[', '[', 'X', ']', '-', 'X', ']', '-', 'F', '[', '-', 'F', 'X', ']', '+', 'X']




In :

def draw_fractal_plant(draw, plant, pos: tuple, angle=0):
LINE_LENGTH = 5
skip = 0
count = 0

for i, val in enumerate(plant):
#print(skip)
count += 1
if skip > 0:
skip -= 1
continue
elif val not in variables and val not in constants:
raise Exception("{} not in the alphabet".format(val))
elif val in constants:
if val == '+':
elif val == '-':
elif val == '[':
skip = draw_fractal_plant(draw, plant[i+1:], (pos, pos), angle)
elif val == ']':
return count
elif val == 'X':
continue
elif val == 'F':
new_pos =  (pos + LINE_LENGTH*cos(angle*(pi/180)),pos + LINE_LENGTH*sin(angle*(pi/180)))
draw.line([pos, new_pos], fill=(0, 0, 0))
#print(new_pos)
pos = new_pos




In :

NB_ITERATIONS = 6

res = axiom
for i in range(1, NB_ITERATIONS):
res = list(itertools.chain(*[rules(x) for x in res]))
img = Image.new('RGB', (500, 500), (255, 255, 255))
draw = ImageDraw.Draw(img)
draw_fractal_plant(draw, res, (0, 250), 25)
img




Out:



## Dragon Curve



In :

# L-system definition
variables = ['X', 'Y']
constants = ['-', '+', 'F']
axiom = ['F', 'X']
def rules(val):
# verify that given var is in the system alphabet
if val not in variables and val not in constants:
raise Exception("{} not in the alphabet".format(val))
if val in constants:
return []
elif val == 'X':
return list('X+YF+')
elif val == 'Y':
return list('-FX-Y')




In :

def rec_draw_dragon_curve(draw, vals, pos: tuple, angle=0, depth=0, max_depth=3):
LINE_LENGTH = 10

if depth >= max_depth:
return angle, pos

for val in vals:
if val == '+':
elif val == '-':
elif val == 'F':
new_pos =  (pos + LINE_LENGTH*cos(angle*(pi/180)),pos + LINE_LENGTH*sin(angle*(pi/180)))
draw.line([pos, new_pos], fill=(0, 0, 255))
pos = new_pos
angle, pos = rec_draw_dragon_curve(draw, rules(val), pos, angle, depth=depth+1, max_depth=max_depth)
return angle, pos




In :

img = Image.new('RGB', (700, 500), (255, 255, 255))
draw = ImageDraw.Draw(img)
rec_draw_dragon_curve(draw, axiom, (450, 150), 90, 0, max_depth=11)
img




Out:



# Spirograph

A spirograph is a drawing tool based on mathematical roulette curves.



In :

class Spirograph:
def __init__(self, origin, R, r, d, angle, theta):
self.origin = origin
self.R = R
self.r = r
self.d = d
self.angle = angle
self.theta = theta

def update(self):
self.angle += self.theta



## Hypotrochoid

Roulette curve defined by

$$x(\theta )=(R-r)\cos \theta +d\cos \left({R-r \over r}\theta \right)$$$$y(\theta )=(R-r)\sin \theta -d\sin \left({R-r \over r}\theta \right)$$


In :

%matplotlib notebook
fig, ax = plt.subplots(dpi=120, figsize=(5, 5))
img_size = 500
img = Image.new('RGB', (img_size, img_size), 'white')
origin = np.array([img_size//2, img_size//2])
spirograph = Spirograph(origin=origin, R=125, r=75, d=125, angle=0, theta=0.2)
im = ax.imshow(img)
plt.axis('off')

def animate(i, img, im, spirograph):
#img = Image.new('RGB', (img_size, img_size), 'white')
draw = ImageDraw.Draw(img)
origin = spirograph.origin
R = spirograph.R
r = spirograph.r
d = spirograph.d
angle = spirograph.angle
# draw main circle
#draw.ellipse([tuple(origin-R), tuple(origin+R)], outline=(0, 0, 255))
# draw inside circle
circle_2_pos = origin + (R - r) * np.array([np.cos(angle), np.sin(angle)])
#draw.ellipse([tuple(circle_2_pos-r), tuple(circle_2_pos+r)], outline=(255, 0, 0))
# draw hypotrochoid
point_x = circle_2_pos + d * np.cos(((R-r)/r)*angle)
point_y = circle_2_pos - d * np.sin(((R-r)/r)*angle)
point = np.array([point_x, point_y])
draw.ellipse([tuple(point-2), tuple(point+2)], fill='black')
#draw.line([tuple(circle_2_pos), tuple(point)], fill='black')
im.set_data(img)
spirograph.update()

ani = animation.FuncAnimation(fig, animate, frames=500, interval=50,
fargs=[img, im, spirograph])




var element = $('#7f733294-d440-4182-be85-2eb732f4ceaa'); /* Put everything inside the global mpl namespace */ window.mpl = {}; mpl.get_websocket_type = function() { if (typeof(WebSocket) !== 'undefined') { return WebSocket; } else if (typeof(MozWebSocket) !== 'undefined') { return MozWebSocket; } else { alert('Your browser does not have WebSocket support.' + 'Please try Chrome, Safari or Firefox ≥ 6. ' + 'Firefox 4 and 5 are also supported but you ' + 'have to enable WebSockets in about:config.'); }; } mpl.figure = function(figure_id, websocket, ondownload, parent_element) { this.id = figure_id; this.ws = websocket; this.supports_binary = (this.ws.binaryType != undefined); if (!this.supports_binary) { var warnings = document.getElementById("mpl-warnings"); if (warnings) { warnings.style.display = 'block'; warnings.textContent = ( "This browser does not support binary websocket messages. " + "Performance may be slow."); } } this.imageObj = new Image(); this.context = undefined; this.message = undefined; this.canvas = undefined; this.rubberband_canvas = undefined; this.rubberband_context = undefined; this.format_dropdown = undefined; this.image_mode = 'full'; this.root =$('<div/>');
this._root_extra_style(this.root)
this.root.attr('style', 'display: inline-block');

$(parent_element).append(this.root); this._init_header(this); this._init_canvas(this); this._init_toolbar(this); var fig = this; this.waiting = false; this.ws.onopen = function () { fig.send_message("supports_binary", {value: fig.supports_binary}); fig.send_message("send_image_mode", {}); if (mpl.ratio != 1) { fig.send_message("set_dpi_ratio", {'dpi_ratio': mpl.ratio}); } fig.send_message("refresh", {}); } this.imageObj.onload = function() { if (fig.image_mode == 'full') { // Full images could contain transparency (where diff images // almost always do), so we need to clear the canvas so that // there is no ghosting. fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height); } fig.context.drawImage(fig.imageObj, 0, 0); }; this.imageObj.onunload = function() { fig.ws.close(); } this.ws.onmessage = this._make_on_message_function(this); this.ondownload = ondownload; } mpl.figure.prototype._init_header = function() { var titlebar =$(
'<div class="ui-dialog-titlebar ui-widget-header ui-corner-all ' +
'ui-helper-clearfix"/>');
var titletext = ( '<div class="ui-dialog-title" style="width: 100%; ' + 'text-align: center; padding: 3px;"/>'); titlebar.append(titletext) this.root.append(titlebar); this.header = titletext; } mpl.figure.prototype._canvas_extra_style = function(canvas_div) { } mpl.figure.prototype._root_extra_style = function(canvas_div) { } mpl.figure.prototype._init_canvas = function() { var fig = this; var canvas_div =('<div/>');

canvas_div.attr('style', 'position: relative; clear: both; outline: 0');

function canvas_keyboard_event(event) {
return fig.key_event(event, event['data']);
}

canvas_div.keydown('key_press', canvas_keyboard_event);
canvas_div.keyup('key_release', canvas_keyboard_event);
this.canvas_div = canvas_div
this._canvas_extra_style(canvas_div)
this.root.append(canvas_div);

var canvas = $('<canvas/>'); canvas.addClass('mpl-canvas'); canvas.attr('style', "left: 0; top: 0; z-index: 0; outline: 0") this.canvas = canvas; this.context = canvas.getContext("2d"); var backingStore = this.context.backingStorePixelRatio || this.context.webkitBackingStorePixelRatio || this.context.mozBackingStorePixelRatio || this.context.msBackingStorePixelRatio || this.context.oBackingStorePixelRatio || this.context.backingStorePixelRatio || 1; mpl.ratio = (window.devicePixelRatio || 1) / backingStore; var rubberband =$('<canvas/>');
rubberband.attr('style', "position: absolute; left: 0; top: 0; z-index: 1;")

var pass_mouse_events = true;

canvas_div.resizable({
start: function(event, ui) {
pass_mouse_events = false;
},
resize: function(event, ui) {
fig.request_resize(ui.size.width, ui.size.height);
},
stop: function(event, ui) {
pass_mouse_events = true;
fig.request_resize(ui.size.width, ui.size.height);
},
});

function mouse_event_fn(event) {
if (pass_mouse_events)
return fig.mouse_event(event, event['data']);
}

rubberband.mousedown('button_press', mouse_event_fn);
rubberband.mouseup('button_release', mouse_event_fn);
// Throttle sequential mouse events to 1 every 20ms.
rubberband.mousemove('motion_notify', mouse_event_fn);

rubberband.mouseenter('figure_enter', mouse_event_fn);
rubberband.mouseleave('figure_leave', mouse_event_fn);

canvas_div.on("wheel", function (event) {
event = event.originalEvent;
event['data'] = 'scroll'
if (event.deltaY < 0) {
event.step = 1;
} else {
event.step = -1;
}
mouse_event_fn(event);
});

canvas_div.append(canvas);
canvas_div.append(rubberband);

this.rubberband = rubberband;
this.rubberband_canvas = rubberband;
this.rubberband_context = rubberband.getContext("2d");
this.rubberband_context.strokeStyle = "#000000";

this._resize_canvas = function(width, height) {
// Keep the size of the canvas, canvas container, and rubber band
// canvas in synch.
canvas_div.css('width', width)
canvas_div.css('height', height)

canvas.attr('width', width * mpl.ratio);
canvas.attr('height', height * mpl.ratio);
canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');

rubberband.attr('width', width);
rubberband.attr('height', height);
}

// Set the figure to an initial 600x600px, this will subsequently be updated
// upon first draw.
this._resize_canvas(600, 600);

// Disable right mouse context menu.
$(this.rubberband_canvas).bind("contextmenu",function(e){ return false; }); function set_focus () { canvas.focus(); canvas_div.focus(); } window.setTimeout(set_focus, 100); } mpl.figure.prototype._init_toolbar = function() { var fig = this; var nav_element =$('<div/>')
nav_element.attr('style', 'width: 100%');
this.root.append(nav_element);

// Define a callback function for later on.
function toolbar_event(event) {
return fig.toolbar_button_onclick(event['data']);
}
function toolbar_mouse_event(event) {
return fig.toolbar_button_onmouseover(event['data']);
}

for(var toolbar_ind in mpl.toolbar_items) {
var name = mpl.toolbar_items[toolbar_ind];
var tooltip = mpl.toolbar_items[toolbar_ind];
var image = mpl.toolbar_items[toolbar_ind];
var method_name = mpl.toolbar_items[toolbar_ind];

if (!name) {
// put a spacer in here.
continue;
}
var button = $('<button/>'); button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' + 'ui-button-icon-only'); button.attr('role', 'button'); button.attr('aria-disabled', 'false'); button.click(method_name, toolbar_event); button.mouseover(tooltip, toolbar_mouse_event); var icon_img =$('<span/>');

var tooltip_span = $('<span/>'); tooltip_span.addClass('ui-button-text'); tooltip_span.html(tooltip); button.append(icon_img); button.append(tooltip_span); nav_element.append(button); } var fmt_picker_span =$('<span/>');

var fmt_picker = $('<select/>'); fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content'); fmt_picker_span.append(fmt_picker); nav_element.append(fmt_picker_span); this.format_dropdown = fmt_picker; for (var ind in mpl.extensions) { var fmt = mpl.extensions[ind]; var option =$(
'<option/>', {selected: fmt === mpl.default_extension}).html(fmt);
fmt_picker.append(option)
}

// Add hover states to the ui-buttons
$( ".ui-button" ).hover( function() {$(this).addClass("ui-state-hover");},
function() { $(this).removeClass("ui-state-hover");} ); var status_bar =$('<span class="mpl-message"/>');
nav_element.append(status_bar);
this.message = status_bar;
}

mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {
// Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,
// which will in turn request a refresh of the image.
this.send_message('resize', {'width': x_pixels, 'height': y_pixels});
}

mpl.figure.prototype.send_message = function(type, properties) {
properties['type'] = type;
properties['figure_id'] = this.id;
this.ws.send(JSON.stringify(properties));
}

mpl.figure.prototype.send_draw_message = function() {
if (!this.waiting) {
this.waiting = true;
this.ws.send(JSON.stringify({type: "draw", figure_id: this.id}));
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
var format_dropdown = fig.format_dropdown;
var format = format_dropdown.options[format_dropdown.selectedIndex].value;
}

mpl.figure.prototype.handle_resize = function(fig, msg) {
var size = msg['size'];
if (size != fig.canvas.width || size != fig.canvas.height) {
fig._resize_canvas(size, size);
fig.send_message("refresh", {});
};
}

mpl.figure.prototype.handle_rubberband = function(fig, msg) {
var x0 = msg['x0'] / mpl.ratio;
var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;
var x1 = msg['x1'] / mpl.ratio;
var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;
x0 = Math.floor(x0) + 0.5;
y0 = Math.floor(y0) + 0.5;
x1 = Math.floor(x1) + 0.5;
y1 = Math.floor(y1) + 0.5;
var min_x = Math.min(x0, x1);
var min_y = Math.min(y0, y1);
var width = Math.abs(x1 - x0);
var height = Math.abs(y1 - y0);

fig.rubberband_context.clearRect(
0, 0, fig.canvas.width, fig.canvas.height);

fig.rubberband_context.strokeRect(min_x, min_y, width, height);
}

mpl.figure.prototype.handle_figure_label = function(fig, msg) {
}

mpl.figure.prototype.handle_cursor = function(fig, msg) {
var cursor = msg['cursor'];
switch(cursor)
{
case 0:
cursor = 'pointer';
break;
case 1:
cursor = 'default';
break;
case 2:
cursor = 'crosshair';
break;
case 3:
cursor = 'move';
break;
}
fig.rubberband_canvas.style.cursor = cursor;
}

mpl.figure.prototype.handle_message = function(fig, msg) {
fig.message.textContent = msg['message'];
}

mpl.figure.prototype.handle_draw = function(fig, msg) {
// Request the server to send over a new figure.
fig.send_draw_message();
}

mpl.figure.prototype.handle_image_mode = function(fig, msg) {
fig.image_mode = msg['mode'];
}

mpl.figure.prototype.updated_canvas_event = function() {
// Called whenever the canvas gets updated.
this.send_message("ack", {});
}

// A function to construct a web socket function for onmessage handling.
// Called in the figure constructor.
mpl.figure.prototype._make_on_message_function = function(fig) {
return function socket_on_message(evt) {
if (evt.data instanceof Blob) {
/* FIXME: We get "Resource interpreted as Image but
* transferred with MIME type text/plain:" errors on
* Chrome.  But how to set the MIME type?  It doesn't seem
* to be part of the websocket stream */
evt.data.type = "image/png";

/* Free the memory for the previous frames */
if (fig.imageObj.src) {
(window.URL || window.webkitURL).revokeObjectURL(
fig.imageObj.src);
}

fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(
evt.data);
fig.updated_canvas_event();
fig.waiting = false;
return;
}
else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == "data:image/png;base64") {
fig.imageObj.src = evt.data;
fig.updated_canvas_event();
fig.waiting = false;
return;
}

var msg = JSON.parse(evt.data);
var msg_type = msg['type'];

// Call the  "handle_{type}" callback, which takes
// the figure and JSON message as its only arguments.
try {
var callback = fig["handle_" + msg_type];
} catch (e) {
console.log("No handler for the '" + msg_type + "' message type: ", msg);
return;
}

if (callback) {
try {
// console.log("Handling '" + msg_type + "' message: ", msg);
callback(fig, msg);
} catch (e) {
console.log("Exception inside the 'handler_" + msg_type + "' callback:", e, e.stack, msg);
}
}
};
}

// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas
mpl.findpos = function(e) {
//this section is from http://www.quirksmode.org/js/events_properties.html
var targ;
if (!e)
e = window.event;
if (e.target)
targ = e.target;
else if (e.srcElement)
targ = e.srcElement;
if (targ.nodeType == 3) // defeat Safari bug
targ = targ.parentNode;

// jQuery normalizes the pageX and pageY
// pageX,Y are the mouse positions relative to the document
// offset() returns the position of the element relative to the document
var x = e.pageX - $(targ).offset().left; var y = e.pageY -$(targ).offset().top;

return {"x": x, "y": y};
};

/*
* return a copy of an object with only non-object keys
* we need this to avoid circular references
* http://stackoverflow.com/a/24161582/3208463
*/
function simpleKeys (original) {
return Object.keys(original).reduce(function (obj, key) {
if (typeof original[key] !== 'object')
obj[key] = original[key]
return obj;
}, {});
}

mpl.figure.prototype.mouse_event = function(event, name) {
var canvas_pos = mpl.findpos(event)

if (name === 'button_press')
{
this.canvas.focus();
this.canvas_div.focus();
}

var x = canvas_pos.x * mpl.ratio;
var y = canvas_pos.y * mpl.ratio;

this.send_message(name, {x: x, y: y, button: event.button,
step: event.step,
guiEvent: simpleKeys(event)});

/* This prevents the web browser from automatically changing to
* the text insertion cursor when the button is pressed.  We want
* to control all of the cursor setting manually through the
* 'cursor' event from matplotlib */
event.preventDefault();
return false;
}

mpl.figure.prototype._key_event_extra = function(event, name) {
// Handle any extra behaviour associated with a key event
}

mpl.figure.prototype.key_event = function(event, name) {

// Prevent repeat events
if (name == 'key_press')
{
if (event.which === this._key)
return;
else
this._key = event.which;
}
if (name == 'key_release')
this._key = null;

var value = '';
if (event.ctrlKey && event.which != 17)
value += "ctrl+";
if (event.altKey && event.which != 18)
value += "alt+";
if (event.shiftKey && event.which != 16)
value += "shift+";

value += 'k';
value += event.which.toString();

this._key_event_extra(event, name);

this.send_message(name, {key: value,
guiEvent: simpleKeys(event)});
return false;
}

mpl.figure.prototype.toolbar_button_onclick = function(name) {
this.handle_save(this, null);
} else {
this.send_message("toolbar_button", {name: name});
}
};

mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {
this.message.textContent = tooltip;
};
mpl.toolbar_items = [["Home", "Reset original view", "fa fa-home icon-home", "home"], ["Back", "Back to  previous view", "fa fa-arrow-left icon-arrow-left", "back"], ["Forward", "Forward to next view", "fa fa-arrow-right icon-arrow-right", "forward"], ["", "", "", ""], ["Pan", "Pan axes with left mouse, zoom with right", "fa fa-arrows icon-move", "pan"], ["Zoom", "Zoom to rectangle", "fa fa-square-o icon-check-empty", "zoom"], ["", "", "", ""], ["Download", "Download plot", "fa fa-floppy-o icon-save", "download"]];

mpl.extensions = ["eps", "jpeg", "pdf", "png", "ps", "raw", "svg", "tif"];

mpl.default_extension = "png";var comm_websocket_adapter = function(comm) {
// Create a "websocket"-like object which calls the given IPython comm
// object with the appropriate methods. Currently this is a non binary
// socket, so there is still some room for performance tuning.
var ws = {};

ws.close = function() {
comm.close()
};
ws.send = function(m) {
//console.log('sending', m);
comm.send(m);
};
// Register the callback with on_msg.
comm.on_msg(function(msg) {
//console.log('receiving', msg['content']['data'], msg);
// Pass the mpl event to the overridden (by mpl) onmessage function.
ws.onmessage(msg['content']['data'])
});
return ws;
}

mpl.mpl_figure_comm = function(comm, msg) {
// This is the function which gets called when the mpl process
// starts-up an IPython Comm through the "matplotlib" channel.

var id = msg.content.data.id;
// Get hold of the div created by the display call when the Comm
// socket was opened in Python.
var element = $("#" + id); var ws_proxy = comm_websocket_adapter(comm) function ondownload(figure, format) { window.open(figure.imageObj.src); } var fig = new mpl.figure(id, ws_proxy, ondownload, element.get(0)); // Call onopen now - mpl needs it, as it is assuming we've passed it a real // web socket which is closed, not our websocket->open comm proxy. ws_proxy.onopen(); fig.parent_element = element.get(0); fig.cell_info = mpl.find_output_cell("<div id='" + id + "'></div>"); if (!fig.cell_info) { console.error("Failed to find cell for figure", id, fig); return; } var output_index = fig.cell_info var cell = fig.cell_info; }; mpl.figure.prototype.handle_close = function(fig, msg) { var width = fig.canvas.width/mpl.ratio fig.root.unbind('remove') // Update the output cell to use the data from the current canvas. fig.push_to_output(); var dataURL = fig.canvas.toDataURL(); // Re-enable the keyboard manager in IPython - without this line, in FF, // the notebook keyboard shortcuts fail. IPython.keyboard_manager.enable()$(fig.parent_element).html('<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">');
fig.close_ws(fig, msg);
}

mpl.figure.prototype.close_ws = function(fig, msg){
fig.send_message('closing', msg);
// fig.ws.close()
}

mpl.figure.prototype.push_to_output = function(remove_interactive) {
// Turn the data on the canvas into data in the output cell.
var width = this.canvas.width/mpl.ratio
var dataURL = this.canvas.toDataURL();
this.cell_info['text/html'] = '<amp-img layout="responsive" width="500" height="300" src="' + dataURL + '" width="' + width + '">';
}

mpl.figure.prototype.updated_canvas_event = function() {
// Tell IPython that the notebook contents must change.
IPython.notebook.set_dirty(true);
this.send_message("ack", {});
var fig = this;
// Wait a second, then push the new image to the DOM so
// that it is saved nicely (might be nice to debounce this).
setTimeout(function () { fig.push_to_output() }, 1000);
}

mpl.figure.prototype._init_toolbar = function() {
var fig = this;

var nav_element = $('<div/>') nav_element.attr('style', 'width: 100%'); this.root.append(nav_element); // Define a callback function for later on. function toolbar_event(event) { return fig.toolbar_button_onclick(event['data']); } function toolbar_mouse_event(event) { return fig.toolbar_button_onmouseover(event['data']); } for(var toolbar_ind in mpl.toolbar_items){ var name = mpl.toolbar_items[toolbar_ind]; var tooltip = mpl.toolbar_items[toolbar_ind]; var image = mpl.toolbar_items[toolbar_ind]; var method_name = mpl.toolbar_items[toolbar_ind]; if (!name) { continue; }; var button =$('<button class="btn btn-default" href="#" title="' + name + '"><i class="fa ' + image + ' fa-lg"></i></button>');
button.click(method_name, toolbar_event);
button.mouseover(tooltip, toolbar_mouse_event);
nav_element.append(button);
}

var status_bar = ('<span class="mpl-message" style="text-align:right; float: right;"/>'); nav_element.append(status_bar); this.message = status_bar; // Add the close button to the window. var buttongrp =('<div class="btn-group inline pull-right"></div>');
var button = $('<button class="btn btn-mini btn-primary" href="#" title="Stop Interaction"><i class="fa fa-power-off icon-remove icon-large"></i></button>'); button.click(function (evt) { fig.handle_close(fig, {}); } ); button.mouseover('Stop Interaction', toolbar_mouse_event); buttongrp.append(button); var titlebar = this.root.find($('.ui-dialog-titlebar'));
titlebar.prepend(buttongrp);
}

mpl.figure.prototype._root_extra_style = function(el){
var fig = this
el.on("remove", function(){
fig.close_ws(fig, {});
});
}

mpl.figure.prototype._canvas_extra_style = function(el){
// this is important to make the div 'focusable
el.attr('tabindex', 0)
// reach out to IPython and tell the keyboard manager to turn it's self
// off when our div gets focus

// location in version 3
if (IPython.notebook.keyboard_manager) {
IPython.notebook.keyboard_manager.register_events(el);
}
else {
// location in version 2
IPython.keyboard_manager.register_events(el);
}

}

mpl.figure.prototype._key_event_extra = function(event, name) {
var manager = IPython.notebook.keyboard_manager;
if (!manager)
manager = IPython.keyboard_manager;

// Check for shift+enter
if (event.shiftKey && event.which == 13) {
this.canvas_div.blur();
event.shiftKey = false;
// Send a "J" for go to next cell
event.which = 74;
event.keyCode = 74;
manager.command_mode();
manager.handle_keydown(event);
}
}

mpl.figure.prototype.handle_save = function(fig, msg) {
}

mpl.find_output_cell = function(html_output) {
// Return the cell and output element which can be found *uniquely* in the notebook.
// Note - this is a bit hacky, but it is done because the "notebook_saving.Notebook"
// IPython event is triggered only after the cells have been serialised, which for
// our purposes (turning an active figure into a static one), is too late.
var cells = IPython.notebook.get_cells();
var ncells = cells.length;
for (var i=0; i<ncells; i++) {
var cell = cells[i];
if (cell.cell_type === 'code'){
for (var j=0; j<cell.output_area.outputs.length; j++) {
var data = cell.output_area.outputs[j];
if (data.data) {
// IPython >= 3 moved mimebundle to data attribute of output
data = data.data;
}
if (data['text/html'] == html_output) {
return [cell, data, j];
}
}
}
}
}

// Register the function which deals with the matplotlib target/channel.
// The kernel may be null if the page has been refreshed.
if (IPython.notebook.kernel != null) {
IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);
}