We shall not cease from exploring,
and the end of all our exploring,
will be to arrive where we started,
and know the place for the first time.
-T.S.Eliot.

Labyrinths and mazes cradle millennia of legend and lore in their twisted articulations.
This page is an ongoing meander.

 

Organic Labyrinths & Mazes [Paper][Color Plate] [Video][Amazing!][Image Gallery] NPAR 2006.

 
 


Tantric symbol from 18th century manuscript.
Copyright © 2002 Hermann Kern, All Rights Reserved.

 

Semantically, a labyrinth is a path that simply winds its way from start to finish, which are often the same place. A maze has forks, dead ends and sometimes  cycles.

Philosophically, labyrinths and mazes are yin and yang. The spiritual labyrinth is a meditative path laid out with careful artistic intent to set you free, while the puzzling maze is a challenging structure designed to trick and entrap. This duality is echoed mathematically using the same of set of curves to define labyrinth or maze topology: labyrinth are the curves while mazes are the space between.

 

Artistically, these structures are immortalized in the work of Salvador Dali, M.C. Escher and Keith Haring. They continue to fuel the imagination of the deliciously twisted doodlers of the MAD magazine and contemporary artists like Adrian Fisher, Christopher Morrison, David Anson Russo, Christopher Berg and Mo Morales.

Visually, we categorize labyrinths and mazes as structured or organic. Structured mazes, often seen in puzzle books, are constructed on geometric grids and have paths precisely aligned with grid cells. Organic labyrinths and mazes, seen mostly in maze art and spiritual symbolism like the Tantric structure (left) have an amorphous visual appearance resembling shapes seen in nature.

 

 

Labyrinths are often considered mankind's first creation borne purely of human imagination. We generate labyrinths using a dynamic curve simulation evolving under forces similar to those seen in nature, hence the term organic. One could hypothesize that the earliest known labyrinths were inspired by such physical formations, even though the Illuminati have for centuries secretly protected the well known fact that the Chartres 11circuit labyrinth is a Martian fingerprint.

Below are some images of curves evolving under parameters of Brownian motion, local smoothness, branching frequency and attraction-repulsion.

 
 
   
 

...a T evolves

...a T wraps toroidally and stabilizes

 

 
  ...a T crossing
...a cross evolves
 ...a triangle evolves
   
   
...a crossed triangle evolves
...osculating circles
 
  ...osculating circles evolve
...a spiral
...biker bunny tattoo: 2 circles & ears
...3 pronged ears ...octopus
...octopus II
...vortex
Copyright © 2006 Karan Singh and Hans Pedersen, All Rights Reserved    
 
 

 

 

Throw in some literature and words become an artistic tool ... phrasing and punctuation guiding the shape and precise length of the resulting labyrinth.

 

 


Copyright © 2006 Karan Singh and Hans Pedersen, All Rights Reserved.

 
 

 

Jabberwocky along the perimeter enclosing  To a Mouse by Robbie Burns a lament to rats in a maze, or if you look closer...

 

Copyright © 2006 Karan Singh and Hans Pedersen, All Rights Reserved.

 To a Mouse with a different tail  by Karan Singh.

   

 

 

Throw in some imagery and pictures guide the labyrinth evolution based on intensity value and gradient ...

   
Copyright
© 2006 Karan Singh and Hans Pedersen, All Rights Reserved.
     
 

 

In an interactive setting the approach transcends a static image filter by offering the designer an opportunity of aesthetically controlling the simulation while watching it grow, retarding or freezing areas and fiddling with simulation parameters.



Copyright © 2006 Karan Singh and Hans Pedersen, All Rights Reserved.
Amazing Grace

 

 

In an interactive setting the approach transcends a static image filter by offering the designer an opportunity of aesthetically controlling the simulation while watching it grow, retarding or freezing areas and fiddling with simulation parameters.

Then again curves that crawl about on a plane could just as well evolve on 3D geometry.


Copyright © 2006 Karan Singh and Hans Pedersen, All Rights Reserved.

 


...a growing list of labyrinthine links:

   

Contemporary maze artists

Mo Morales

Christopher Berg

David Anson Russo

Christopher Morrison

Jody Hall's Mazoons

Adrian Fisher

Sooner Magazine, Spring 2002 - Pavel Tchelitchew

 

Fractals, space filling curves and other math shenanigans

Hilbert Curve Coloring

TSP Art

Folding and unfolding

Ken Perlin's 3D maze applet

 

 

 

 

 

Copyright © 2006 Karan Singh and Hans Pedersen, All Rights Reserved.