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GrantTrebbin/IndexingDemo_BinaryVersion.py

Created March 16, 2017 12:59
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Rendering Animations for Hilbert Curves - Undocumented Scratch Code
Raw
IndexingDemo_BinaryVersion.py
import svgwrite
import math
# mogrify -format gif *.svg
# gifsicle --scale 0.2 --delay=5 --loop --optimize=2 --colors=256 --multifile *.gif > OutGIF/out.gif
order = 3
number_of_index_bits = order * 2
number_of_elements = pow(2, number_of_index_bits)
x_offset = 130
y_offset = 130
class Diagram:
def __init__(self, width, height):
self.width = width
self.height = height
self.dwg = svgwrite.Drawing(profile='full',
size=(str(width) + 'px',
str(height) + 'px'),
viewBox=('0 0 ' + str(width) +
' ' + str(height)))
self.dwg.add(self.dwg.rect(insert=(0, 0),
size=(width, height),
fill='rgb(50,50,50)'))
def coordinate_transform(width, height, size, cells, offset):
return lambda v: [(v[0] + 0.5) * size / cells + offset[0],
size - (v[1] + 0.5) * size / cells + offset[1]]
def draw_grid(d, size, number_of_cells, position):
ct = coordinate_transform(d.width, d.height, size, number_of_cells, position)
d.dwg.add(d.dwg.rect(insert=(position[0], position[1]),
size=(size, size),
stroke='rgb(200,200,200)',
stroke_width=5,
fill='none'))
for i in range(1, number_of_cells):
offset = size * i / number_of_cells
d.dwg.add(d.dwg.line(start=(position[0], position[1] + offset),
end=(position[0] + size, position[1] + offset),
stroke='rgb(200,200,200)',
stroke_width=5))
d.dwg.add(d.dwg.line(start=(position[0] + offset, position[1]),
end=(position[0] + offset, position[1] + size),
stroke='rgb(200,200,200)',
stroke_width=5))
return ct
binary_index = []
for i in range(0, number_of_elements):
binary_list = []
temp = i
for element in range(0, number_of_index_bits):
binary_list.append(temp % 2)
temp //= 2
binary_list.reverse()
x_bin = binary_list[0::2]
y_bin = binary_list[1::2]
x = 0
for bit in x_bin:
x *= 2
x += bit
y = 0
for bit in y_bin:
y *= 2
y += bit
binary_strings = {'index': i,
'binary': binary_list,
'x': x,
'x_bin': x_bin,
'y': y,
'y_bin': y_bin}
binary_index.append(binary_strings)
diagram = Diagram(1920*2, 1080*2)
grid_coord_transform = draw_grid(diagram,
1900,
pow(2, order),
(x_offset, y_offset))
title = diagram.dwg.add(
diagram.dwg.text(
"Binary Indexing",
insert=(x_offset + 2000, y_offset + 130),
fill="rgb(200,200,200)",
style="font-size:180px; font-family:Lucida Console; font-weight:bold"))
attribution = diagram.dwg.add(
diagram.dwg.text(
"@GPTreb",
insert=(x_offset + 3100, y_offset + 1900),
fill="rgb(200,200,200)",
style="font-size:100px; font-family:Lucida Console; font-weight:bold"))
index_name = diagram.dwg.add(
diagram.dwg.text(
"Index",
insert=(x_offset + 2300, y_offset + 500),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
index_num = diagram.dwg.add(
diagram.dwg.text(
"",
insert=(x_offset + 2300, y_offset + 700),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
binary_name = diagram.dwg.add(
diagram.dwg.text(
"Index",
insert=(x_offset + 2300, y_offset + 1000),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
binary_num = diagram.dwg.add(
diagram.dwg.text(
"0b",
insert=(x_offset + 2300, y_offset + 1200),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
x_name = diagram.dwg.add(
diagram.dwg.text(
"x=0b",
insert=(x_offset + 2300, y_offset + 1500),
fill="rgb(200,100,100)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
y_name = diagram.dwg.add(
diagram.dwg.text(
"y=0b",
insert=(x_offset + 2300, y_offset + 1700),
fill="rgb(100,100,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
circle = diagram.dwg.add(diagram.dwg.circle(r=30,
fill="rgb(100,200,100)"))
path = []
trajectory = diagram.dwg.add(
diagram.dwg.polyline(
points=[(0, 0)],
stroke="rgb(100,200,100)",
stroke_linejoin='round',
stroke_width=15,
fill='none'))
frame = 0
index_bits = []
for i in range(0, number_of_index_bits):
temp = diagram.dwg.add(
diagram.dwg.text(
"1",
insert=(x_offset + 2520+i*110, y_offset + 1200),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
index_bits.append(temp)
for step in range(0, number_of_elements):
digits = math.ceil(math.log10(number_of_elements))
format_string = '{0:0>' + str(digits) + '}'
index_num.text = format_string.format(step)
index_bit_list = binary_index[step]['binary']
for i in range(0, number_of_index_bits):
index_bits[i].text = index_bit_list[i]
if (i % 2) == 0:
index_bits[i]['fill'] = "rgb(200,100,100)"
else:
index_bits[i]['fill'] = "rgb(100,100,200)"
x_binary = binary_index[step]['x_bin']
x_dec = binary_index[step]['x']
y_binary = binary_index[step]['y_bin']
y_dec = binary_index[step]['y']
x_string = ''.join([str(e) for e in x_binary])
y_string = ''.join([str(e) for e in y_binary])
x_name.text = 'x=0b' + x_string
y_name.text = 'y=0b' + y_string
if step < number_of_elements-1:
next_x_dec = binary_index[step+1]['x']
next_y_dec = binary_index[step+1]['y']
transition_steps = int(math.sqrt(pow((next_y_dec-y_dec), 2) +
pow((next_x_dec-x_dec), 2))/0.1)
for i in range(0, transition_steps):
transitional_x = (transition_steps-i) * x_dec + i * next_x_dec
transitional_y = (transition_steps-i) * y_dec + i * next_y_dec
dot_coordinates = grid_coord_transform(
(transitional_x / transition_steps,
transitional_y / transition_steps))
coordinate_tuple = tuple(dot_coordinates)
path.append(coordinate_tuple)
trajectory.points = path
circle['cx'] = dot_coordinates[0]
circle['cy'] = dot_coordinates[1]
diagram.dwg.filename = format(frame, '04') + '.svg'
diagram.dwg.save()
frame += 1
else:
transitional_x = x_dec
transitional_y = y_dec
dot_coordinates = grid_coord_transform((x_dec, y_dec))
coordinate_tuple = tuple(dot_coordinates)
path.append(coordinate_tuple)
trajectory.points = path
circle['cx'] = dot_coordinates[0]
circle['cy'] = dot_coordinates[1]
for end_frames in range(0, 20):
diagram.dwg.filename = format(frame, '04') + '.svg'
diagram.dwg.save()
frame += 1
Raw
IndexingDemo_GrayCode.py
import svgwrite
import math
# mogrify -format gif *.svg
# gifsicle --scale 0.2 --delay=5 --loop --optimize=2 --colors=256 --multifile *.gif > OutGIF/out.gif
order = 3
number_of_index_bits = order * 2
number_of_elements = pow(2, number_of_index_bits)
x_offset = 130
y_offset = 130
class Diagram:
def __init__(self, width, height):
self.width = width
self.height = height
self.dwg = svgwrite.Drawing(profile='full',
size=(str(width) + 'px',
str(height) + 'px'),
viewBox=('0 0 ' + str(width) +
' ' + str(height)))
self.dwg.add(self.dwg.rect(insert=(0, 0),
size=(width, height),
fill='rgb(50,50,50)'))
def coordinate_transform(width, height, size, cells, offset):
return lambda v: [(v[0] + 0.5) * size / cells + offset[0],
size - (v[1] + 0.5) * size / cells + offset[1]]
def draw_grid(d, size, number_of_cells, position):
ct = coordinate_transform(d.width, d.height, size, number_of_cells, position)
d.dwg.add(d.dwg.rect(insert=(position[0], position[1]),
size=(size, size),
stroke='rgb(200,200,200)',
stroke_width=5,
fill='none'))
for i in range(1, number_of_cells):
offset = size * i / number_of_cells
d.dwg.add(d.dwg.line(start=(position[0], position[1] + offset),
end=(position[0] + size, position[1] + offset),
stroke='rgb(200,200,200)',
stroke_width=5))
d.dwg.add(d.dwg.line(start=(position[0] + offset, position[1]),
end=(position[0] + offset, position[1] + size),
stroke='rgb(200,200,200)',
stroke_width=5))
return ct
binary_index = []
for i in range(0, number_of_elements):
binary_list = []
temp = i
for element in range(0, number_of_index_bits):
binary_list.append(temp % 2)
temp //= 2
binary_list.reverse()
gray_list = [binary_list[0]] + [abs(binary_list[j+1]-binary_list[j]) for j in range(number_of_index_bits-1)]
print(binary_list)
print(gray_list)
print("---")
x_bin = gray_list[0::2]
y_bin = gray_list[1::2]
x = 0
for bit in x_bin:
x *= 2
x += bit
y = 0
for bit in y_bin:
y *= 2
y += bit
binary_strings = {'index': i,
'binary': binary_list,
'gray': gray_list,
'x': x,
'x_bin': x_bin,
'y': y,
'y_bin': y_bin}
binary_index.append(binary_strings)
diagram = Diagram(1920*2, 1080*2)
grid_coord_transform = draw_grid(diagram,
1900,
pow(2, order),
(x_offset, y_offset))
title = diagram.dwg.add(
diagram.dwg.text(
"Gray Code Indexing",
insert=(x_offset + 2000, y_offset + 100),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
attribution = diagram.dwg.add(
diagram.dwg.text(
"@GPTreb",
insert=(x_offset + 3100, y_offset + 1900),
fill="rgb(200,200,200)",
style="font-size:100px; font-family:Lucida Console; font-weight:bold"))
index_name = diagram.dwg.add(
diagram.dwg.text(
"Index",
insert=(x_offset + 2000, y_offset + 450),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
index_num = diagram.dwg.add(
diagram.dwg.text(
"",
insert=(x_offset + 2000, y_offset + 650),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
binary_name = diagram.dwg.add(
diagram.dwg.text(
"Gray code of Index",
insert=(x_offset + 2000, y_offset + 1000),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
binary_num = diagram.dwg.add(
diagram.dwg.text(
"0b",
insert=(x_offset + 2000, y_offset + 1200),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
x_name = diagram.dwg.add(
diagram.dwg.text(
"x=0b",
insert=(x_offset + 2000, y_offset + 1500),
fill="rgb(200,100,100)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
y_name = diagram.dwg.add(
diagram.dwg.text(
"y=0b",
insert=(x_offset + 2000, y_offset + 1700),
fill="rgb(100,100,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
circle = diagram.dwg.add(diagram.dwg.circle(r=30,
fill="rgb(100,200,100)"))
path = []
trajectory = diagram.dwg.add(
diagram.dwg.polyline(
points=[(0, 0)],
stroke="rgb(100,200,100)",
stroke_linejoin='round',
stroke_width=15,
fill='none'))
frame = 0
index_bits = []
for i in range(0, number_of_index_bits):
temp = diagram.dwg.add(
diagram.dwg.text(
"1",
insert=(x_offset + 2220+i*110, y_offset + 1200),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
index_bits.append(temp)
for step in range(0, number_of_elements):
digits = math.ceil(math.log10(number_of_elements))
format_string = '{0:0>' + str(digits) + '}'
index_num.text = format_string.format(step)
index_bit_list = binary_index[step]['gray']
for i in range(0, number_of_index_bits):
index_bits[i].text = index_bit_list[i]
if (i % 2) == 0:
index_bits[i]['fill'] = "rgb(200,100,100)"
else:
index_bits[i]['fill'] = "rgb(100,100,200)"
x_binary = binary_index[step]['x_bin']
x_dec = binary_index[step]['x']
y_binary = binary_index[step]['y_bin']
y_dec = binary_index[step]['y']
x_string = ''.join([str(e) for e in x_binary])
y_string = ''.join([str(e) for e in y_binary])
x_name.text = 'x=0b' + x_string
y_name.text = 'y=0b' + y_string
marker_coordinates = grid_coord_transform((x_dec, y_dec))
diagram.dwg.add(diagram.dwg.circle(center=marker_coordinates,
r=30,
fill="rgb(100,200,100)"))
if step < number_of_elements-1:
next_x_dec = binary_index[step+1]['x']
next_y_dec = binary_index[step+1]['y']
transition_steps = int(math.sqrt(pow((next_y_dec-y_dec), 2) +
pow((next_x_dec-x_dec), 2))/0.1)
for i in range(0, transition_steps):
transitional_x = (transition_steps-i) * x_dec + i * next_x_dec
transitional_y = (transition_steps-i) * y_dec + i * next_y_dec
dot_coordinates = grid_coord_transform(
(transitional_x / transition_steps,
transitional_y / transition_steps))
coordinate_tuple = tuple(dot_coordinates)
path.append(coordinate_tuple)
trajectory.points = path
circle['cx'] = dot_coordinates[0]
circle['cy'] = dot_coordinates[1]
diagram.dwg.filename = format(frame, '04') + '.svg'
diagram.dwg.save()
frame += 1
else:
transitional_x = x_dec
transitional_y = y_dec
dot_coordinates = grid_coord_transform((x_dec, y_dec))
coordinate_tuple = tuple(dot_coordinates)
path.append(coordinate_tuple)
trajectory.points = path
circle['cx'] = dot_coordinates[0]
circle['cy'] = dot_coordinates[1]
for end_frames in range(0, 20):
diagram.dwg.filename = format(frame, '04') + '.svg'
diagram.dwg.save()
frame += 1
Raw
IndexingDemo_Hilbert.py
import svgwrite
import math
import colorsys
# mogrify -format gif *.svg
# gifsicle --scale 0.2 --delay=5 --loop --optimize=2 --colors=256 --multifile *.gif > OutGIF/out.gif
order = 4
number_of_index_bits = order * 2
number_of_elements = pow(2, number_of_index_bits)
x_offset = 130
y_offset = 130
class BinaryCoordinate:
def __init__(self, index, bits_per_dimension, dimensions):
self.number_of_bits = dimensions * bits_per_dimension
self.original_bits = []
self.index = index
self.dimensions = dimensions
self.bits_per_dimension = bits_per_dimension
temporary_index = self.index
for bit_index in range(0, self.number_of_bits):
self.original_bits.append(temporary_index % 2)
temporary_index //= 2
self.original_bits.reverse()
self.bits = self.original_bits
def dimension_subset_binary(self, dimension_number):
subset = self.bits[dimension_number:
self.number_of_bits:
self.dimensions]
return subset
def dimension_subset_decimal(self, dimension_number):
subset = self.dimension_subset_binary(dimension_number)
decimal = 0
for bit_index in subset:
decimal = decimal * 2 + bit_index
return decimal
def swap_lower_bits(self, dimension_1, dimension_2, offset):
for bit_index in range(offset * self.dimensions,
self.number_of_bits,
self.dimensions):
temporary_bit = self.bits[bit_index +
dimension_1]
self.bits[bit_index + dimension_1] =\
self.bits[bit_index + dimension_2]
self.bits[bit_index + dimension_2] = \
temporary_bit
def invert_lower_bits(self, dimension, offset):
for bit_index in range(offset * self.dimensions,
self.number_of_bits,
self.dimensions):
temporary_bit = self.bits[bit_index +
dimension]
self.bits[bit_index + dimension] = (-1) * temporary_bit + 1
def gray(bits):
gray_bits = [bits[0]] +\
[abs(bits[j + 1] - bits[j]) for j in range(len(bits) - 1)]
return gray_bits
class Diagram:
def __init__(self, width, height):
self.width = width
self.height = height
self.dwg = svgwrite.Drawing(profile='full',
size=(str(width) + 'px',
str(height) + 'px'),
viewBox=('0 0 ' + str(width) +
' ' + str(height)))
self.dwg.add(self.dwg.rect(insert=(0, 0),
size=(width, height),
fill='rgb(50,50,50)'))
def coordinate_transform(size, cells, offset):
return lambda v: [(v[0] + 0.5) * size / cells + offset[0],
size - (v[1] + 0.5) * size / cells + offset[1]]
def draw_grid(d, size, number_of_cells, position):
ct = coordinate_transform(size, number_of_cells, position)
d.dwg.add(d.dwg.rect(insert=(position[0], position[1]),
size=(size, size),
stroke='rgb(200,200,200)',
stroke_width=1,
fill='none'))
for i in range(1, number_of_cells):
offset = size * i / number_of_cells
d.dwg.add(d.dwg.line(start=(position[0], position[1] + offset),
end=(position[0] + size, position[1] + offset),
stroke='rgb(200,200,200)',
stroke_width=1))
d.dwg.add(d.dwg.line(start=(position[0] + offset, position[1]),
end=(position[0] + offset, position[1] + size),
stroke='rgb(200,200,200)',
stroke_width=1))
return ct
diagram = Diagram(1920*2, 1080*2)
line_1 = diagram.dwg.add(
diagram.dwg.text(
'Gray Code to',
insert=(x_offset + 2000, y_offset + 100),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
line_2 = diagram.dwg.add(
diagram.dwg.text(
'Hilbert Curve',
insert=(x_offset + 2000, y_offset + 350),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
line_3 = diagram.dwg.add(
diagram.dwg.text(
'via the',
insert=(x_offset + 2000, y_offset + 600),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
line_4 = diagram.dwg.add(
diagram.dwg.text(
'Skilling Method',
insert=(x_offset + 2000, y_offset + 850),
fill="rgb(200,200,200)",
style="font-size:150px; font-family:Lucida Console; font-weight:bold"))
attribution = diagram.dwg.add(
diagram.dwg.text(
"@GPTreb",
insert=(x_offset + 3100, y_offset + 1900),
fill="rgb(200,200,200)",
style="font-size:100px; font-family:Lucida Console; font-weight:bold"))
grid_coord_transform = draw_grid(diagram,
1900,
pow(2, order),
(x_offset, y_offset))
elements = []
path = []
circles = []
lines = []
frame = 0
for element in range(0, number_of_elements):
new_element = BinaryCoordinate(element, order, 2)
new_element.bits = gray(new_element.bits)
elements.append(new_element)
x_coord = new_element.dimension_subset_decimal(0)
y_coord = new_element.dimension_subset_decimal(1)
coordinates = grid_coord_transform((x_coord, y_coord))
path.append(tuple(coordinates))
for element_index in range(0, number_of_elements):
progress_fraction = element_index/number_of_elements
hue = 40*progress_fraction + 216*(1-progress_fraction)
rgb_color = colorsys.hsv_to_rgb(hue/256, 0.4, 0.9)
color_string = 'rgb(' +\
str(int(rgb_color[0]*256)) +\
',' +\
str(int(rgb_color[1]*256)) + \
',' +\
str(int(rgb_color[2]*256)) + ')'
coordinate_1 = path[element_index]
new_marker = diagram.dwg.add(diagram.dwg.circle(center=coordinate_1,
r=15,
fill=color_string))
circles.append(new_marker)
if element_index < number_of_elements-1:
coordinate_2 = path[element_index+1]
new_line = diagram.dwg.add(diagram.dwg.line(start=coordinate_1,
end=coordinate_1,
stroke=color_string,
stroke_linecap='round',
stroke_width=8,
fill='none'))
length = math.sqrt(pow((coordinate_1[0]-coordinate_2[0]), 2) +
pow((coordinate_1[1]-coordinate_2[1]), 2))
number_of_steps = int(length / 500) + 1
for step in range(0, number_of_steps):
line_progress = (step+1)/number_of_steps
new_line['x2'] = (1-line_progress)*coordinate_1[0] +\
line_progress*coordinate_2[0]
new_line['y2'] = (1-line_progress)*coordinate_1[1] +\
line_progress*coordinate_2[1]
diagram.dwg.filename = format(frame, '04') + '.svg'
diagram.dwg.save()
frame += 1
lines.append(new_line)
diagram.dwg.filename = format(frame, '04') + '.svg'
diagram.dwg.save()
frame += 1
path_progression = []
path_progression.append(path)
path_progression.append(path)
path_progression.append(path)
#1****************************************************************
path_progression.append([])
for element in elements:
if element.bits[5] == 0:
element.swap_lower_bits(1, 0, 3)
else:
element.invert_lower_bits(0, 3)
x_coord = element.dimension_subset_decimal(0)
y_coord = element.dimension_subset_decimal(1)
coordinates = grid_coord_transform((x_coord, y_coord))
path_progression[-1].append(tuple(coordinates))
path_progression.append(path_progression[-1])
#2****************************************************************
path_progression.append([])
for element in elements:
if element.bits[4] == 0:
element.swap_lower_bits(0, 0, 3)
else:
element.invert_lower_bits(0, 3)
x_coord = element.dimension_subset_decimal(0)
y_coord = element.dimension_subset_decimal(1)
coordinates = grid_coord_transform((x_coord, y_coord))
path_progression[-1].append(tuple(coordinates))
path_progression.append(path_progression[-1])
#3****************************************************************
path_progression.append([])
for element in elements:
if element.bits[3] == 0:
element.swap_lower_bits(1, 0, 2)
else:
element.invert_lower_bits(0, 2)
x_coord = element.dimension_subset_decimal(0)
y_coord = element.dimension_subset_decimal(1)
coordinates = grid_coord_transform((x_coord, y_coord))
path_progression[-1].append(tuple(coordinates))
path_progression.append(path_progression[-1])
#4****************************************************************
path_progression.append([])
for element in elements:
if element.bits[2] == 0:
element.swap_lower_bits(0, 0, 2)
else:
element.invert_lower_bits(0, 2)
x_coord = element.dimension_subset_decimal(0)
y_coord = element.dimension_subset_decimal(1)
coordinates = grid_coord_transform((x_coord, y_coord))
path_progression[-1].append(tuple(coordinates))
path_progression.append(path_progression[-1])
#5****************************************************************
path_progression.append([])
for element in elements:
if element.bits[1] == 0:
element.swap_lower_bits(1, 0, 1)
else:
element.invert_lower_bits(0, 1)
x_coord = element.dimension_subset_decimal(0)
y_coord = element.dimension_subset_decimal(1)
coordinates = grid_coord_transform((x_coord, y_coord))
path_progression[-1].append(tuple(coordinates))
path_progression.append(path_progression[-1])
#6****************************************************************
path_progression.append([])
for element in elements:
if element.bits[0] == 0:
element.swap_lower_bits(0, 0, 1)
else:
element.invert_lower_bits(0, 1)
x_coord = element.dimension_subset_decimal(0)
y_coord = element.dimension_subset_decimal(1)
coordinates = grid_coord_transform((x_coord, y_coord))
path_progression[-1].append(tuple(coordinates))
path_progression.append(path_progression[-1])
path_progression.append(path_progression[-1])
path_progression.append(path_progression[-1])
for path_number in range(len(path_progression)-1):
for step in range(25):
b = step/25
a = 1 - b
for coordinate in range(0, number_of_elements):
circles[coordinate]['cx'] = \
a * path_progression[path_number][coordinate][0] +\
b * path_progression[path_number+1][coordinate][0]
circles[coordinate]['cy'] =\
a * path_progression[path_number][coordinate][1] +\
b * path_progression[path_number+1][coordinate][1]
for coordinate in range(0, number_of_elements-1):
lines[coordinate]['x1'] =\
a * path_progression[path_number][coordinate][0] +\
b * path_progression[path_number + 1][coordinate][0]
lines[coordinate]['y1'] =\
a * path_progression[path_number][coordinate][1] +\
b * path_progression[path_number + 1][coordinate][1]
lines[coordinate]['x2'] =\
a * path_progression[path_number][coordinate + 1][0] +\
b * path_progression[path_number + 1][coordinate + 1][0]
lines[coordinate]['y2'] =\
a * path_progression[path_number][coordinate + 1][1] +\
b * path_progression[path_number + 1][coordinate + 1][1]
diagram.dwg.filename = format(frame, '04') + '.svg'
diagram.dwg.save()
frame += 1
a = BinaryCoordinate(2519, 6, 2)
print(a.bits)
a.swap_lower_bits(1, 0, 0)
print(a.bits)
a.invert_lower_bits(1, 2)
print(a.bits)
print(a.dimension_subset_decimal(0))
print(a.dimension_subset_decimal(1))
print(a.bits)
a.bits = gray(a.bits)
print(a.bits)
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