I did a maze thing ages ago that could support any number of dimensions, but it was very slow to generate. To get an idea of how it generally works with the multiplier and stuff, here's a gif of something I made with it:

One thing that always bugged me was I couldn't figure out pathfinding, and I thought there'd be some cool looking intricate paths between some stuff. I asked about that (since I'm stuck at home doing nothing due to having a broken wrist), and someone suggested linked lists, so I rewrote it all, and managed to get pathfinding between two points working fairly easily.

However, since I'd made the nearest neighbour check run by default, checking for collisions was a huge bottleneck. I tried to optimise it a little, by only doing the pythagoras stuff if the highest coordinate difference was within the combined size of two nodes, which did speed it up like 2x, but it was still quite slow.

Someone else suggested that's what you use trees for, and since I have no idea how KD trees work (and also the list is constantly being added to), I spent a good few hours yesterday making an octree that would work in any dimension, so I could find which nodes are near to then narrow down what the collision function has to check through. The result was like 2.5x faster at 1000 nodes, but exponentially going up to like 10x faster at 8000 nodes, which I'm pretty happy with.

I've just got it fully working and cleaned up now, so I'm looking for a bit of feedback on either my writing style or anything that could be improved. Also, before the line length is mentioned, I decided to do 100 instead of 80.

from __future__ import division
import random
import cPickle

class Node(object):
    """Store the data for each node."""

    def __init__(self, id, location, size, distance=0, 
                 parent=None, children=None, tree=None, neighbours=None):
        self.id = id
        self.location = tuple(location)
        self.size = size
        self.parent = parent
        self.distance = distance
        self.children = children if children else []
        self.tree = tree
        self.neighbours = neighbours

    def __repr__(self):
        return ('Node(id={x.id}, ' 
                     'tree={x.tree}, '
                     'distance={x.distance}, '
                     'location={x.location}, '
                     'size={x.size}, '
                     'parent={x.parent}, '
                     'children={x.children}, '

    def update_neighbours(self):
        self.neighbours = len(self.children) + (self.parent is not None)

    def update_parent(self, parent, node_list):
        """Set a new parent and calculate the distance from origin."""
        if parent < 0:
            parent = None
        self.parent = parent
            self.distance = node_list[parent].distance + 1
        except TypeError:
            self.distance = 0

def recursive_pathfind(start, end, node_list, _path=[], _reverse=True, _last_id=None):
    """Recursively find a path between two nodes."""
    _path = _path + [start]

    #Path complete
    if start == end:
        return _path

    #Search parents
    if _reverse:
        parent = node_list[start].parent
        if parent is not None:
            found_path = recursive_pathfind(parent, end, node_list,
                                            _path=_path, _reverse=True, _last_id=start)
            if found_path is not None:
                return found_path

    #Search children
    for node_id in node_list[start].children:
        if node_id != _last_id:
            found_path = recursive_pathfind(node_id, end, node_list, 
                                            _path=_path, _reverse=False, _last_id=start)
            if found_path is not None:
                return found_path
    return None

class CoordinateToSegment(object):
    """Class used for the tree calculations.
    Its main purpose is to find which segment a node would be in, and
    generate the path to it.
    def __init__(self, dimensions, tree_data):
        self.td = tree_data
        self.dimensions = dimensions
        self._range = range(dimensions)
        n = 0

        #Build index of paths
        self.paths = {}
        for path in self._paths():
            self.paths[tuple(path)] = n
            n += 1

    def convert(self, coordinates, point_size):
        """Convert a coordinate into segments."""

        if len(coordinates) != self.dimensions:
            raise ValueError('invalid coordinate size')

        #Find path to each coordinate
        segments = []
        for i in self._range:
            segments.append(self._find_segment(coordinates[i], point_size))

        #Trim them all to the same length
        min_len = min(len(i) for i in segments)
        segments = [tuple(i[:min_len]) for i in segments]

        #Calculate the path IDs
        path = [self.paths[i] for i in zip(*segments)]
        return path

    def reverse(self, segment):
        """Calculate the coordinates from a segment.
        This only gives a rough value, and is only needed for debugging.
        #Find path from the path index IDs
        segments = [k for i in segment for k, v in self.paths.iteritems() if v == i]

        #Split into separate coordinates
        joined_segments = []
        for i in range(self.dimensions):
            joined_segments.append([j[i] for j in segments])

        #Calculate where the coordinate is following the path
        totals = []
        for coordinate in joined_segments:
            n = self.td.size - 1
            total = 0
            for i in coordinate:
                total += i * pow(2, n)
                n -= 1
        print totals

    def _paths(self, current_path=None, current_level=0, directions=(-1, 1)):
        """Generate a list of paths in the current dimension.
        This is used to get the path index.
        if current_path is None:
            current_path = []
        if current_level == self.dimensions:
            return [current_path]

        #Repeat recursively until editing current_path[-1]
        return_path = []
        for i in directions:
             return_path += self._paths(current_path + [i], current_level + 1, 

        return return_path

    def _find_segment(self, coordinate, point_size):
        """Convert a number into the correct segment.
        If the maximum tree size changes, this needs to be recalculated.
        This runs until either the minimum size has been hit, or the 
        node is overlapping multiple segments.
        total = 0
        path = []
        coordinate_sort = sorted((coordinate - point_size, coordinate + point_size))

        for i in range(self.td.size - self.td.min - 1):
            current_amount = pow(2, self.td.size - i - 1)

            #Detect whether to end or which way to continue
            if coordinate == total or coordinate_sort[0] <= total <= coordinate_sort[1]:
                return path
            elif coordinate_sort[1] < total:
                total -= current_amount
            elif coordinate_sort[0] > total:
                total += current_amount
                raise ValueError('unknown segment error')

        return path

def get_recursive_items(tree, items=None):
    """Iterate through a list to get all recursive items."""
    if items is None:
        items = []
        for branch in tree:
            items += get_recursive_items(branch)
    except TypeError:
        items += tree
    return items

class TreeData(object):
    """Class to store the tree of points.
    It can work in any dimension, and dynamically grows when needed.

    def __init__(self, generation, start_size, min_size=None):
        self._gen = generation
        self._conversion = CoordinateToSegment(self._gen.dimensions, self)
        if min_size is None:
            min_size = start_size
        self.size = start_size
        self.min = min_size
        self._branch_length = range(len(self._conversion.paths) + 1)
        self.data = [[] for i in self._branch_length]

    def adjust_size(self, coordinate):
        """Increase the size of the tree if needed.
        If the size does change, everything is recalculated.
        start_size = self.size
        highest_coord = max(coordinate)
        lowest_coord = min(coordinate)

        #Increment by 1 until the size fits
        max_range = pow(2, self.size)
        while max_range < highest_coord or -max_range > lowest_coord:
            self.size += 1
            max_range = pow(2, self.size)
        if self.size - start_size:

    def recalculate(self):
        """Recalculate the path to every point."""
        self.data = [[] for i in self._branch_length]
        for node in self._gen.nodes:
            path = self.calculate(node.location, node.size, check_size=False)
            self.add(node, path)

    def add(self, node, path):
        """Add a node to the tree."""
        node.tree = path

    def calculate(self, location, size, check_size=True):
        """Calculate the path to a point with location and size."""
        if check_size:
        path = self._conversion.convert(location, size)
        return path

    def near(self, path):
        """Find all nodes near a path for collision checking.
        Use TreeData.calculate to get the path.
        branch, nodes = self._recursive_branch(path)
        nearby_nodes = get_recursive_items(branch)
        return nearby_nodes + nodes

    def _recursive_branch(self, path):
        """Follows a recursive path to get part of a list.
        If the path goes deeper than the list, new branches of the list
        will be created.
        For collision check purposes, a list of all items found going 
        to that branch is also returned.
        branch = self.data
        nodes = []

        for branch_id in path:
            nodes += branch[-1]

            #Create new branch if it doesn't exist
            if not branch[branch_id]:
                branch[branch_id] = [[] for i in self._branch_length]

            branch = branch[branch_id]
        return branch, nodes

class GenerationCore(object):
    """Create and store the main generation."""

    def __init__(self, dimensions, size=1, min_size=None, multiplier=0.99, 
                 bounds=None, max_retries=None, _nodes=None, _tree_data=None):
        self.nodes = [] if _nodes is None else _nodes
        self.dimensions = dimensions
        self.range = range(dimensions)
        self.directions = self._possible_directions()

        self.size = max(0.001, size)
        self.bounds = bounds
        self.retries = max_retries
        self.multiplier = max(0.001, multiplier)
        self.highest = 0

        if self.retries is None:
            self.retries = self.dimensions

        #Check the bounds are in the correct format
        if self.bounds is not None:
            if len(self.bounds) != 2:
                raise ValueError('bounding box should contain 2 values')
            for item in self.bounds:
                if len(item) != self.dimensions:
                    raise ValueError('incorrect bounding box size')

        #Find out how small the tree needs to go
        if min_size is None:
            min_size = self.size / 20
        self.min_size = max(0.001, min_size)
        min_size_exp = 0
        while pow(2, min_size_exp) > self.min_size:
            min_size_exp -= 1

        #Make the tree cover everything without wasting space
        self.tree = TreeData(self, 0, min_size_exp)
        if _tree_data is not None:
            self.tree.data = _tree_data

    def _possible_directions(self):
        """Build a list of every direction the maze can move in."""
        directions = []
        for i in self.range:
            for j in (-1, 1):
                directions.append([j if i == n else 0 for n in self.range])
        return directions

    def generate(self, max_nodes=None, max_length=None, location=None, min_nodes=None, 
        """Main function to generate the maze."""

        self.nodes = []
        #Sort out number of nodes
        if max_nodes is None:
            if min_nodes is None:
                raise ValueError('either maximum or minimum nodes should be specified')
            max_nodes = min_nodes
        if min_nodes is None:
            min_nodes = 0
        #Take off 1 since total_nodes starts at -1
        max_nodes -= 1
        min_nodes -= 1

        #Make up other values if not specified
        if max_length is None:
            max_length = max_nodes // 5

        #Check the location is in the correct format
        if location is None:
            location = [0.0 for i in generation.range]
        elif len(location) != self.dimensions:
            raise ValueError('invalid coordinates for starting location')

        #General range checks
        min_nodes = max(-1, min_nodes)
        max_nodes = max(min_nodes, max_nodes)
        max_length = max(1, max_length)

        #Start generation
        failed_nodes = current_retries = 0
        current_length = total_nodes = -1
        while (total_nodes + failed_nodes < max_nodes
               or total_nodes < min_nodes and failed_nodes < max_fails):

            #End the branch if too many fails
            if current_retries >= self.retries:
                current_length = max_length
                current_retries = 0
                failed_nodes += 1

            #End the branch if too long
            if current_length >= max_length:
                node_id = random.randint(0, total_nodes)
                current_length = 0
                node_id = total_nodes

            if node_id < 0:
                node_status = self._add_node(location=location)
                node_status = self._add_node(node_id=node_id)

            if node_status == -1:
                current_retries = self.retries
                failed_nodes += 1
            elif node_status == -2:
                current_retries += 1
                total_nodes += 1
                current_length += 1

    def _add_node(self, node_id=None, location=None):
        """Add individual node to the generation.
        Needs either a base node or a location to work off.

        if node_id is None:
            if location is None:
                raise ValueError('location must be defined if no nodes exist')
            new_size = self.size
            new_location = location
            new_id = 0

            node_start = self.nodes[node_id]

            #Get the initial values to create the new node from
            new_size = node_start.size * self.multiplier
            new_id = self.nodes[-1].id + 1

            #End branch now if size is too small
            if new_size < self.min_size:
                return -1

            direction = random.choice(self.directions)
            new_location = tuple(a + b * node_start.size * 2 * max(1, self.multiplier)
                                 for a, b in zip(node_start.location, direction))

        #Check tree for collisions
        node_path = self.tree.calculate(new_location, new_size)
        near_nodes = self.tree.near(node_path)
        if self.collision_check(new_location, new_size, self.bounds, near_nodes):
            return -2

        #Add to original node as child
            node_start.neighbours += 1
        except UnboundLocalError:

        #Create a new node
        new_node = Node(new_id, new_location, new_size, neighbours=node_id is not None)
        new_node.update_parent(node_id, self.nodes)
        if new_node.distance > self.highest:
            self.highest = new_node.distance

        #Update values with new node
        self.tree.add(new_node, node_path)
        return new_id

    def add_branch(self, length=1, node_id=None):
        """Individually add a new branch to the generation."""
        total_directions = len(self.directions)

        #Find a node without any neighbours
        while node_id is None:
            node_id = random.choice(self.nodes).id
            if self.nodes[node_id].neighbours == total_directions:
                node_id = None

        #Draw a path until a limit is reached
        i = 0
        retries = 0
        while i < length:
            node_status = self._add_node(node_id)
            if node_status == -1 or retries > self.retries:
                return i
            elif node_status == -2:
                retries += 1
                node_id = node_status
                retries = 0
                i += 1
        return i

    def collision_check(self, location, size, bounds=None, node_ids=None):
        """Check a new node isn't too close to an existing one.

        The first calculation is a simple range check, if a bounding box
        has been defined.

        The second calculation iterates through all the nodes, and first
        checks that the maximum distance on a single plane isn't over 
        the combined node size. If it is within range, pythagoras is
        used to find and compare the squared distance.

        #Get every node ID if not provided
        if node_ids is None:
            node_ids = range(len(self.nodes))

        #Bounding box search
        if bounds:
            for i in self.range:
                if not bounds[0][i] + size <= location[i] <= bounds[1][i] - size:
                    return True

        #Pythagoras search
        for node_id in node_ids:
            node = self.nodes[node_id]
            size_total = size + node.size
            distance = [abs(a - b) for a, b in zip(location, node.location)]

            #Skip before the calculation if the maximum distance is too far
            if max(distance) > size_total:

            distance_total = sum(pow(i, 2) for i in distance)
            if distance_total < pow(size_total, 2):
                return True

        return False

    def save(self, location):
        save_data = {'Bounds': self.bounds,
                     'Dimensions': self.dimensions,
                     'Min': self.min_size,
                     'Multiplier': self.multiplier,
                     'Nodes': self.nodes,
                     'Retries': self.retries,
                     'Size': self.size,
                     'Tree': self.tree.data}
        with open(location, 'w') as f:

    def load(cls, location):
        with open(location, 'r') as f:
            file_data = cPickle.loads(f.read())
        return cls(bounds=file_data['Bounds'],

    def get_bounds(self):
        """Find the bounds of the generation, including the node size."""
        bounds = [[float('inf') for i in range(self.dimensions)], 
                  [-float('inf') for i in range(self.dimensions)]]
        for node in self.nodes:
            for i, coordinate in enumerate(node.location):
                if bounds[0][i] > coordinate:
                        bounds[0][i] = coordinate - node.size[i]
                    except TypeError:
                        bounds[0][i] = coordinate - node.size
                elif bounds[1][i] < coordinate:
                        bounds[1][i] = coordinate + node.size[i]
                    except TypeError:
                        bounds[1][i] = coordinate + node.size
        bounds = tuple(tuple(i) for i in bounds)
        return bounds

For any Maya users, this doesn't include the animation or colours yet, but here's a class to build it in 3D. You only need to iterate through generation.nodes to use node.location and node.size, so if you have a different 3D software package it'd still be easily possible to display.

def format_coordinate(coordinate, links, default_location=[], default_value=0.0):
    """Reformat a coordinate using the new links.
    For example, the coordinate (-1.0, 0.0, 1.0) with new links as (1, 2, 0, 3)
    will be reformatted as [0.0, 1.0, -1.0, 0.0].
    Always returns a list of len(links) values.

    dimensions = len(coordinate)

    #Trim off any unnecessary coordinates
    n = 0
    for i in links[::-1]:
        if i >= dimensions:
            n += 1
    if n:
        links = links[:-n]

    #Reformat the coordinate
    new_location = [None for i in links]
    for i, j in enumerate(links):
        if j < dimensions:
            new_location[i] = coordinate[j]
                new_location[i] = default_location[i]
                new_location[i] = default_value

    return new_location

class MayaDraw(object):
    """Class to be used for Maya only.
    It handles building cubes and curves to visualise the maze.

    import pymel.core as pm

    def __init__(self, generation, time_stretch=3):
        self._gen = generation
        self._cubes = []
        self._curves = []
        self._paths = []
        self._shaders = []
        self._bounding_box = None
        self._links = range(4)
        self._time_mult = time_stretch

    def cubes(self, colours=None, amount=25):
        """Draw cubes based on information from the nodes.
        As neighbour checking is spherical, there may be some 
        overlapping where corners meet.
        It is here you interpret the dimensions, where currently it has
        support for up to 4 (4th is used for keyframes).

        self.remove(cubes=True, curves=False, paths=False, shaders=True, bounding_box=False)
        default_location = self._gen.nodes[0].location

        for node in self._gen.nodes:
            size = node.size * 1.98
            new_location = format_coordinate(node.location, self._links, default_location)

            #Create new cube
            new_cube = self.pm.polyCube(n='genCube{}'.format(node.id), w=size, h=size, d=size)[0]
            self.pm.move(new_cube, new_location[:3])

            #Set attributes
            self.pm.addAttr(new_cube, sn='gen_id', ln='GenerationID', min=0, at='long')
            self.pm.setAttr('{}.gen_id'.format(new_cube), node.id)
            self.pm.addAttr(new_cube, sn='gen_dist', ln='GenerationDistance', min=0, at='long')
            self.pm.setAttr('{}.gen_dist'.format(new_cube), node.distance)
            self.pm.addAttr(new_cube, sn='gen_parent', ln='GenerationParent', dt='string')
            self.pm.setAttr('{}.gen_parent'.format(new_cube), str(node.parent))
            self.pm.addAttr(new_cube, sn='gen_child', ln='GenerationChildren', dt='string')
            self.pm.setAttr('{}.gen_child'.format(new_cube), ', '.join(map(str, node.children)))
            self.pm.addAttr(new_cube, sn='gen_adj', ln='GenerationNeighbours', min=0, at='long')
            self.pm.setAttr('{}.gen_adj'.format(new_cube), node.neighbours)

            #Set 4th dimension as keys
            if self._gen.dimensions > self._links[3]:
                time_gap = max(1, node.size * 2 * self._time_mult)
                time_start = new_location[3] * self._time_mult
                self.pm.setKeyframe(new_cube, at='v', value=0, time=time_start - time_gap)
                self.pm.setKeyframe(new_cube, at='v', value=1, time=time_start)
                self.pm.setKeyframe(new_cube, at='v', value=0, time=time_start + time_gap)

        self.bounding_box(time_slider=True, draw=False)
        if colours is None:
            colours = ['black', 'white']
        self.update_shaders(colours, amount)

    def update_shaders(self, colours, amount=25):

        shader_name = self._shader_build(colours, amount)

        increment = (amount - 1) / self._gen.highest
        for cube in self._cubes:
            distance = self.pm.getAttr('{}.gen_dist'.format(cube)) * increment
            i = int(round(distance))

    def curves(self):
        """Draw curves by following the path of children.
        Start a new curve when the next ID is no longer a child.
        self.remove(curves=True, cubes=False, paths=False, shaders=False, bounding_box=False)
        default_location = self._gen.nodes[0].location

        #Run through all the points
        curve_list = []
        for i, node in enumerate(self._gen.nodes):

            #Start a new curve
            if node.id not in self._gen.nodes[i-1].children:
                    start_point = self._gen.nodes[self._gen.nodes[i].parent].location
                    start_point = format_coordinate(start_point, self._links, default_location)[:3]
                except TypeError:
                    start_point = []

            new_location = format_coordinate(node.location, self._links, default_location)[:3]

        #Convert to suitable coordinates and draw
        for curves in curve_list:
            if len(curves) > 1:
                converted_coordinates = [coordinate for coordinate in curves if coordinate]
                new_curve = self.pm.curve(p=converted_coordinates, d=1) 

    def path(self, start, end):
        """Draw path between two nodes."""
        nodes = self._gen.nodes
        path = recursive_pathfind(start, end, nodes)
        if path is None:

        curve_points = [format_coordinate(nodes[node_id].location, 
                        for node_id in path]
        self._paths.append(str(self.pm.curve(p=curve_points, d=5)))

    def bounding_box(self, draw=True, time_slider=False):

        default_location = self._gen.nodes[0].location
        bb = [format_coordinate(i, self._links, default_location)
              for i in self._gen.get_bounds()]

        #Draw the box
        if draw:
            self.remove(bounding_box=True, curves=False, cubes=False, paths=False, shaders=False)
            mid_point = [i / 2 for i in (bb[0][i] + bb[1][i] for i in range(3))]
            bb_cube = self.pm.polyCube(w=bb[1][0] - bb[0][0],
                                       h=bb[1][1] - bb[0][1],
                                       d=bb[1][2] - bb[0][2])
            self.pm.move(bb_cube[0], mid_point)
            self._bounding_box = str(bb_cube[0])

        #Update the time slider
        if time_slider and self._gen.dimensions > self._links[3]:
            pm.playbackOptions(min=int(bb[0][3] * self._time_mult - 1), 
                               max=int(bb[1][3] * self._time_mult) + 2)
            pm.currentTime(int(bb[0][3] - 1) * self._time_mult)

        return bb

    def remap_coordinates(self, x=None, y=None, z=None, t=None):
        """Update coordinate links using the input value.
        It will attempt to rearrange them based on the input to not 
        result in any duplicates.
        See format_coordinates() for how the links are used.
        available_links = range(4)

        if x is not None:
            del available_links[available_links.index(x)]
        if y is not None:
            del available_links[available_links.index(y)]
        if z is not None:
            del available_links[available_links.index(z)]
        if t is not None:
            del available_links[available_links.index(t)]
        if x is None:
            x = available_links.pop(0)
        if y is None:
            y = available_links.pop(0)
        if z is None:
            z = available_links.pop(0)
        if t is None:
            t = available_links.pop(0)

        self._links = [x, y, z, t]

    def remove(self, cubes=True, curves=True, paths=True, shaders=True, bounding_box=True):
        """Remove any objects created by this class."""
        scene_objects = set(map(str, self.pm.ls()))
        delete_objects = []
        if cubes:
            for cube in self._cubes:
                if cube in scene_objects:
            self._cubes = []
        if curves:
            for curve in self._curves:
                if curve in scene_objects:
            self._curves = []
        if paths:
            for path in self._paths:
                if path in scene_objects:
            self._paths = []
        if shaders:
            for shader in self._shaders:
                if shader in scene_objects:
            self._shaders = []
        if bounding_box:
            if self._bounding_box in scene_objects:

    def _colour_build(self):
        """Build a dictionary of colours."""

        colour_core = {'BLACK': ((0, 0, 0), 'blk'),
                       'WHITE': ((1, 1, 1), 'wht')}
        colour_main = {'RED': ((1, 0, 0), 'red'),
                       'GREEN': ((0, 1, 0), 'grn'),
                       'BLUE': ((0, 0, 1), 'blu'),
                       'YELLOW': ((1, 1, 0), 'ylw'),
                       'MAGENTA': ((1, 0, 1), 'mgt'),
                       'CYAN':((0, 1, 1), 'cyn')}
        colour_extra = {'ORANGE': ((1, 0.5, 0), 'org'),
                        'PURPLE': ((0.5, 0, 0.5), 'ppl'),
                        'GREY': ((0.5, 0.5, 0.5), 'gry'),
                        'BROWN': ((0.3, 0.2, 0), 'brn')}

        for name, values in dict(colour_main).iteritems():
            value = tuple({0: 0, 1: 0.5}[i] for i in values[0])
            colour_main['DARK{}'.format(name)] = (value, 'd{}'.format(values[1]))

            value = tuple({0: 0.5, 1: 1}[i] for i in values[0])
            colour_main['LIGHT{}'.format(name)] = (value, 'l{}'.format(values[1]))

        for name, values in dict(colour_extra).iteritems():
            value = tuple({0: 0, 0.2: 0.1, 0.3: 0.2, 0.5: 0.3, 0.7: 0.6, 0.8: 0.7, 1: 1}[i] for i in values[0])
            colour_extra['DARK{}'.format(name)] = (value, 'd{}'.format(values[1]))

            value = tuple({0: 0, 0.2: 0.3, 0.3: 0.4, 0.5: 0.7, 0.7: 0.8, 0.8: 0.9, 1: 1}[i] for i in values[0])
            colour_extra['LIGHT{}'.format(name)] = (value, 'l{}'.format(values[1]))

        result = {}
        return result

    def _colour_transition(self, colours, amount):
        """Create a transition between colours.
        Input must be in (R, G, B) format.

        if len(colours) == 1:
            return [colours[0]] * amount

        amount -= 1
        increment = amount / (len(colours) - 1)

        result = []
        for i in range(amount):

            progress = i / increment
            colour_index = int(progress)
            colour_percentage = progress % 1

            colour_current = colours[colour_index]
            colour_next = colours[colour_index + 1]
            difference = [colour_next[0] - colour_current[0],
                          colour_next[1] - colour_current[1],
                          colour_next[2] - colour_current[2]]
            difference = [i * colour_percentage for i in difference]
            result.append(tuple(i + j for i, j in zip(colour_current, difference)))

        return result

    def _shader_build(self, colours, amount):
        """Create the shaders."""

        #Get colour values from input
        colour_dict = self._colour_build()
        valid_colours = []
        for name in colours:
            name_format = name.replace(' ','').upper()
            except KeyError:
        if not valid_colours:
            raise ValueError('no valid colours input')

        #Format name
        name_base = ''.join(name.capitalize() for rgb, name in valid_colours)
        name_surface = "surface{}{}{}".format(name_base, amount, 'n{}')
        name_base = name_base[0].lower() + name_base[1:]
        name_shader = '{}{}{}'.format(name_base, amount, 'n{}')

        #Delete duplicate shaders
        scene_objects = set(map(str, self.pm.ls()))
        delete_list = []
        if name_shader.format(0) in scene_objects:
            for i in range(amount):
                existing_shader = name_shader.format(i)
                if existing_shader in scene_objects:
        if delete_list:

        transitions = self._colour_transition([rgb for rgb, name in valid_colours], amount)
        for i, colour in enumerate(transitions):

            #Create shader
            new_shader = self.pm.shadingNode('lambert', asShader=True, name=name_shader.format(i))
            new_shader.color.set(colour, type='double3')

            #Link with surfaceshader
            new_surface = self.pm.sets(renderable=True, noSurfaceShader=True, empty=True, name=name_surface.format(i))
            self.pm.connectAttr(new_shader.outColor, new_surface.surfaceShader)


        return name_shader

Then this is the actual code to run the functions, I think it should work outside of Maya. max_length is how long forks are allowed to grow before ending, the rest is fairly self explanatory I think.

#Delete previous generation
except NameError:

#Create new generation
dimensions = 4
generation = GenerationCore(dimensions, multiplier=0.98)
generation.generate(min_nodes=10000, max_length=100, max_fails=2000)

#Save/load generation
if False:
    import os
    file_location = os.path.expanduser('~') + '/MazeGen.cache'
    generation = GenerationCore.load(file_location)

#Draw generation in 3D if in Maya
    draw = MayaDraw(generation, time_stretch=10)
except ImportError:
    draw.remap_coordinates(x=3, t=2)
    draw.cubes(amount=100, colours=['white','cyan','purple','white'])
    draw.path(0, generation.nodes[-1].id)

If you set some bounds and the multiplier to 1, it should draw a proper style maze, it's just a bit boring that way.

Since the tree data isn't really stored after the generation, here's an example of what the tree looks like at 3000 nodes in 3D. There's probably a better way of doing it but it worked for me.

One thing I've realised is I may be able to merge CoordinateToSegment with TreeData, but I've given up on coding for now so I dunno yet.

Edit: Added a few extra bits, mainly for Maya.
You can now remap coordinates, so for example, you could use a 3 dimensional generation and swap x with t, so basically you have the 3D generation, but only 2D slices of it that you view by changing the time.
I also added the shaders too, so now you can see 4D generations properly. To be totally honest, I thought they'd look cooler (the 4D generations, not shaders), but they're a bit disappointing haha, but I'll try render a video later to show what it looks like.

If anyone has an idea for the 5th dimension or any others, I'm all ears.

  • 1
    \$\begingroup\$ No time for a review but beautiful animation! \$\endgroup\$
    – SylvainD
    Commented Feb 9, 2016 at 20:38
  • \$\begingroup\$ Haha thanks, the plan was to make a flower when I did that. I didn't link it in the post (I'll do it next time I update it), but here's the full size video if you're interested - youtube.com/watch?v=RkHEVtgiLUA \$\endgroup\$
    – Peter
    Commented Feb 10, 2016 at 20:23

1 Answer 1


The only thing I noticed - you fell into the mutable-default trap, as in:


This should be avoided; for more reading, see http://docs.python-guide.org/en/latest/writing/gotchas/


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