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Page published: Feb 27th, 2021
Last update: May 28th


Latest post:
I'm starting to think that maybe nature uses some of these algorhitms for growth of trees and other plants.
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Watch the longer video with flythrough where these sculptures are more spread on YouTube.


There are:
- Two separate blue corridors (opposed to one another),
- three separate yellow ones (identical to each other but rotated 120 degrees) and
- three separate green ones (counter to yellow corridors).
No matter where you start, each of these eight separate corridors can bring you to the central cell. There are no isolated cells.
The blue corridor could represent the neutral while yellow and green represent the opposing positive/negative corridors.

Other characteristics of this maze


- There is never more than five exits in any given cell.
- It can expand into infinity by following the same algorithm that was used to construct the mazes in videos.
- Space is completely filled by either the yellow, green or blue cell(polyhedron).
- Has plenty of dead ends.
- Every blue cell touches and is at minimum distance with both, a yellow and a green cell. Same goes for every yellow(touches at least one blue and at least one green cell) and every green cell(touches at least one blue and at least one yellow cell).
- No matter of the maze's size(when growing from the central cell), there's always one, but only one, completely straight way through (the blue corridor).


 The algorithm qualities


Can start drawing the maze at any cell and it doesn't require the central cell as a reference point.
Uses integer numbers in computations(also coordinates), therefore
- is very fast and
- no floating point error is present when building large models, precision may be adjusted to any scale.

Where it can be used


Beside computer games, there could be many applications of this maze in real world. With modern 3D printing technology, anything from small scale to building size maze could be printed. Also it could be useful as structure model for mining or a space station. Even in production of explosives - the fuse material can be spread out through exploding material.
I don't know to what extent of precision new materials can be built, but with this technology, incredibly porosive substances could be made.

 

How it came about


My earlier discoveries led me to believe that such a maze exists in 3D space and after around 15 years, I finally came to the solution. Now I'm pretty sure that similiar mazes exist in higher dimensions (4D, 5D, ...).

 

Videos & Animations






Mazes of higher levels

In the near future, I will explain what I mean by levels.


The video above is a representation of the new maze, different to the first one (the one containing green cells).
Watch it on YouTube


Posted on: March 31st
Usually when I discover something new, after playing around for a while, I stumble into visually interesting structures and patterns.
 In the following two videos only the cells that represent dead ends are drawn (cells which touch only one other cell with the same colour). This also proves the correctness, validity, symmetry and perfection of this system.
When you'll understand the mathematics behind it, you'll be really amazed. I haven't published the algorithm yet. It's actually really simple math - the world gravitates towards simplicity.

(Click on videos to play/pause them)
 
The video below shows the same path, but with perspective.  
 
 
 
These videos are also available on on my YouTube channel.
The video on the top of the page also shows only 'dead ends', but of a different maze (level).


  I'm quite sure that similiar mazes exist in higher dimensions (4D, 5D, ...).


 

Future R&D

With the achieved know-how I can now theoretically construct infinite amount of new different 3D mazes. Same characteristics would apply to them, they'd only differ in cellular structure. I don't yet know what they will appear like, it's too hard to visualize without building a 3D model first. And I don't mean just manually modifying the existing maze, I'm intending to make programs with algorithms that will build mazes differently. If what I can say about these upcoming mazes:
- Every next one will have longer straight corridors and
- none of them will have that one straight way through them as it is in this maze(shown in the video).
I was wrong about this last statement; every next maze will have it.
 Videos of new mazes are soon to come.