Wikimore

Summary

Description

Matrix showing the same elements and some of the symmetry

Petrie polygon graph of the 8-dimensional cube, the Hasse diagram of an 8 element set's power set

Compare the Petrie polygon graph of the 4-dimensional cube:

The colors represent the Walsh equivalence classes of 3-ary Boolean functions.

Simpler Python code is shown in this file. It makes use of code created with the Python code below.

Source

Own work

Author

Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

Other versions

Quality image

This image has been assessed using the Quality image guidelines and is considered a Quality image.

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Category:Quality images#Octeract%20Petrie%20polygon.svg Category:Quality images missing SDC depicts Category:Quality images missing SDC creator Category:Quality images missing SDC inception

Source code

Python and SVG source

from sympy import cos, pi
from math import log
from my.own.stuff import number_to_reverse_binary_list, hypercube_edges
import psycopg2


con = psycopg2.connect(host='lukulhuft', database='hupu', user='tupu', password='lupu')
cur = con.cursor()
bg_colors = ['fd0', 'e60000', 'bbb', '666', 'ffb4b4']

angle = pi / 16
a = cos(angle)
b = cos(3*angle)
c = cos(5*angle)
d = cos(7*angle)
directions = [
    [-a, d], [-b, c], [-c, b], [-d, a], [d, a], [c, b], [b, c], [a, d]
]  # directions of the 8 edges leaving the lowest vertex (as sympy objects)

big_factor = 1000 / (a + b + c + d)  # diameter of the whole diagram shall be 2000
tiny_factor = 0.029  # the tiny dots in the vertices must be slightly off center


################################## vertices ##################################

sym_coordinates = []  # sympy objects
svg_coordinates = []  # rounded and converted to strings

svg_vertices = ''
svg_numbers = ''

for i in range(256):

    cur.execute("""select wec from boolf3 where numval = %s""" % (i))
    bg_color_index = cur.fetchone()[0] + 1  # from the DB comes a value between -1 and 3
    bg_color = bg_colors[bg_color_index]

    binary_vector = number_to_reverse_binary_list(i, 8)

    x_sym = 0
    y_sym = 0
    for j in range(8):
        if binary_vector[j]:
            x_sym += directions[j][0]
            y_sym += directions[j][1]
    x_svg = str(round(big_factor * x_sym, 3))
    y_svg = str(round(-big_factor * y_sym + 1000, 3))

    sym_coordinates.append({'x': x_sym, 'y': y_sym})
    svg_coordinates.append({'x': x_svg, 'y': y_svg})

    svg_vertices += '<circle cx="%s" cy="%s" r="14.5" fill="#%s"/>' % (x_svg, y_svg, bg_color)
    svg_numbers += '<text x="%s" y="%s">%s</text>' % (x_svg, y_svg, i)


################################## edges ##################################

svg_edges = ''
svg_tiny_dots = ''
edges = hypercube_edges(8)

for edge in edges:  # ``edge`` is a pair of integers between 0 and 255

    bottom = edge[0]
    top = edge[1]

    bottom_x_svg = svg_coordinates[bottom]['x']
    bottom_y_svg = svg_coordinates[bottom]['y']
    top_x_svg = svg_coordinates[top]['x']
    top_y_svg = svg_coordinates[top]['y']

    svg_edges += '<line x1="%s" y1="%s" x2="%s" y2="%s"/>' % (bottom_x_svg, bottom_y_svg, top_x_svg, top_y_svg)

    edge_direction = directions[int(log(bottom ^ top, 2))]

    tiny_edge_direction_x = tiny_factor * edge_direction[0]
    tiny_edge_direction_y = tiny_factor * edge_direction[1]

    bottom_x_sym = sym_coordinates[bottom]['x']
    bottom_y_sym = sym_coordinates[bottom]['y']
    top_x_sym = sym_coordinates[top]['x']
    top_y_sym = sym_coordinates[top]['y']

    bottom_tiny_x_sym = bottom_x_sym + tiny_edge_direction_x
    bottom_tiny_y_sym = bottom_y_sym + tiny_edge_direction_y
    top_tiny_x_sym = top_x_sym - tiny_edge_direction_x
    top_tiny_y_sym = top_y_sym - tiny_edge_direction_y

    bottom_tiny_x_svg = str(round(big_factor * bottom_tiny_x_sym, 3))
    bottom_tiny_y_svg = str(round(-big_factor * bottom_tiny_y_sym + 1000, 3))
    top_tiny_x_svg = str(round(big_factor * top_tiny_x_sym, 3))
    top_tiny_y_svg = str(round(-big_factor * top_tiny_y_sym + 1000, 3))

    svg_tiny_dots += '<circle cx="%s" cy="%s" r="1.8"/><circle cx="%s" cy="%s" r="1.8"/> ' % \
                     (bottom_tiny_x_svg, bottom_tiny_y_svg, top_tiny_x_svg, top_tiny_y_svg)


################################## file ##################################

svg_string = """<?xml version="1.0" encoding="UTF-8"?>
<svg xmlns="http://www.w3.org/2000/svg" width="2100" height="2100" viewBox="-1050 -1050 2100 2100">

    <!-- edges -->
    <g style="stroke:#000; stroke-width:1.5; stroke-opacity:0.5;">
        %s
    </g>

    <!-- vertices -->
    <g style="stroke:#000; stroke-width:1.5px;">
        %s
    </g>

    <!-- tiny dots -->
    %s

    <!-- numbers -->
    <g style="text-anchor: middle; letter-spacing: -1;" font-size="10px" font-family="sans-serif" transform="translate(0, 3.7)" fill-opacity="0.5">
        %s
    </g>

</svg>
""" % (svg_edges, svg_vertices, svg_tiny_dots, svg_numbers)

svg_file = open('Octeract Petrie polygon.svg', 'w')
svg_file.write(svg_string)

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.

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Category:3-ary Boolean functions in octeract graph Category:3-ary Boolean functions; tribes

Wikimore

File:Octeract Petrie polygon.svg

Summary

Source code

Licensing