Maze of the Week #91 - Monte Alban Maze

Maze of the Week #91 keeps us in Mexico for my 3rd different maze of a pyramid or ruin with this Monte Alban Maze from the Zapotec archeological site in Oaxaca, Mexico. Here are my other 2 similar mazes:

Chichen Itza Maze

Mayan Ruins at Uxmal Maze

Photos: I had a chance to visit the site because I lived in the city for 3 months. Here is a gallery of pictures I took, one of which was used to make the maze. I went on a day with perfect weather - easy to do around there - and was one of the first 5 people in the site, so my pictures include very few people !

YouTube: Here is a quick 6 minute video showing the grounds if the pictures weren’t enough.

The Maze: I re-worked this maze after finishing it. A small re-color and then I re-sized it from paper size to a size that fit the structure/maze better. I also added shadows which were a huge improvement IMO.

Monte Alban Maze

I hope you enjoy the maze. Maze download is available on the homepage. Check out my YouTube channel where you can watch mazes being made and solved !!!

Coming next week:

A maze of an auditorium

Image-Guided Maze Construction Research Paper

I was doing some exploring as I wrote a series of articles on the use of AI and creating mazes and found a paper from July 2007 on Image-Guided Maze Construction. The authors were Jie Xu and Craig S Kaplan from the University of Waterloo. Basically they looked into creating maze art using algorithms and computer graphics. They did a wonderful 25 minute video explaining the concept which is worth watching. You can find the paper and the original video at this link.

What does the paper say ?

The paper "Image-Guided Maze Construction" by Jie Xu and Craig S. Kaplan presents a technique for automatically synthesizing pictorial mazes from images. The system allows the designer to manually partition an image into a set of regions and assign style parameters to each region. They are also able to sketch a schematic layout for the maze's solution path. The final maze will contain intertwined passages in each region, connected together by breaking walls between regions.

The paper describes four different maze textures: directional mazes, spiral mazes, random mazes, and user-defined lines. Each texture is controlled by specialized parameters. The paper also describes an algorithm for building mazes that respect the layout of a given solution tree.

The system has been implemented as an interactive application. The paper presents several examples of mazes generated by the system, including mazes based on photographs of the Great Wall of China, a portrait, and a discus thrower.

So why do I bring this to your attention so many years later ?

Well because of these 3 blog posts I wrote:

• WHAT I LEARNED USING AI TO MAKE MAZE ART

• COMPARISON OF 12 AI GENERATING WEBSITES - WHO DID MAZES THE BEST ?

• MAZE ART: ADVANCED TIPS TO CREATING YOUR OWN MASTERPIECE

And when you combine the ideas of those 3 posts with this research paper and I come to the following conclusion: AI will be reading things like this paper and will be making great mazes soon. I can image someone like these authors working with AI and teaching it to make maze art relatively quickly IF they want to take the time to do it. Will it change what this site looks like ? Only time will tell. Maybe it becomes the typewriter in the year 2000. Let’s hope not !

Side note: I used Starryai to generate the picture for this blog using this prompt:

Make me a logo for a blog post titled Image-Guided Maze Construction paper. This is what it came up with.

Exploring Different Ways to Solve a Maze

So you want to solve a maze and could use some extra help. Or, more likely you are writing a computer program and want to know what options you have to solve a maze. I will take you through 8 popular maze solving methods and then discuss some of the the other most common everyday ways of solving mazes people use and give you some cheat codes. Here is what you can expect:

8 MAZE SOLVING METHODS

• 4 METHODS FOR PHYSICAL MAZES SOLVED FROM THE INSIDE

• 4 METHODS FOR MAZES VIEWED FROM ABOVE

5 COMMON MAZE SOLVING OPTIONS

2 CHEAT CODES TO SOLVE MAZES

8 MAZE SOLVING METHODS

Let’s start with 4 methods used for physical mazes, like a hedge or corn maze, where you do not know what the maze looks like, i.e. you are a traveler in a maze looking to find the exit or goal.

• Random Mouse Method - Very basic way to solve a maze and probably the way you typically do it. Starting walking, and randomly pick a direction at each intersection you reach. Nothing fancy, and not efficient, but works eventually. Also works for regular mazes you see from above - and probably how you solve most puzzle mazes.

• Wall Follower Method - Well known way to solve a maze where you follow a wall consistently through a maze until you solve it. It can be a left handed or a right handed method, but once you choose your side you must stick with it ! To use this the maze must be simply connected, meaning it has no loops and all walls are attached to the outer walls of the maze.

• Pledge Algorithm Method - A wall following method that can deal with disjointed walls. It involves counting turns you make (clockwise turn is positive, counter-clockwise turn is negative) and making decisions based on getting the number back to zero. Here are rules to follow to use it in practice:

  • Start at the entrance of the maze.

  • Move forward until a wall is encountered.

  • Follow the wall on the right-hand side until you reach the exit.

  • If you encounter a disjoint wall, you should turn left and continue following the wall on its right-hand side. How do you know you have a disjointed wall ? You arrive back at the same spot in a disjointed wall (a loop).

  • If you return to the starting point without finding the exit, turn around and follow the wall on its left-hand side until it reaches a new path. Then, it should follow the wall on its right-hand side again.

  • Repeat steps 3-5 until you reach the exit.

• Trémaux's Algorithm - Uses a set of rules to solve a maze:

  • If you visit a junction with new paths, pick one at random.

  • Cross it out as you explore.

  • If you reach a dead end, retrace your steps to the last junction with unexplored paths and choose another path.

  • If you reach a junction with all paths already explored, retrace your steps to the last junction with unexplored paths and choose another path.

The following 4 methods of solving a maze are useful for typical puzzle mazes where you can see the complete maze from above:

• Reverse Solve (Dead-end filling) - In this method you start at a known dead end and color in the pathway until you reach a junction. Eventually this process leads to a maze completely filled in expect for the correct pathway ! I like to use this for hidden message mazes !

• Recursive algorithm - Math, coding. That is where this algorithm comes in. It uses X and Y values to check each spot inside a maze and determine if the space has been visited yet or not. It marks incorrect solutions as it goes and if it finds the correct pathway it marks in the X/Y values (pathway) of how it got there.

• Maze-routing algorithm - Commonly used in chip design but can be used to solve a maze also. It is not something a person would use unless they coded it into a program. It works by finding the distant between any 2 points in the maze, blah, blah, blah, look you solved the maze !

• Shortest Path Algorithms - A collection of many algorithms which all attempt to do the same thing - find the shortest path between 2 points - like let’s say the start and the goal ! While the details of this set of algorithms may not be for the average person to use to solve a maze, be glad it is used whenever you need directions between 2 points (Google Maps !, etc.)

Now let’s look more specifically at real world examples and the methods most people actually use for puzzle mazes. What method do you use to solve drawn mazes ?

5 COMMON MAZE SOLVING OPTIONS

• With a writing utensil - probably the most common way to solve a drawn maze. You have a maze printed out or in a book in front of you and you grab a pen or pencil and solve using it. Makes the maze a one time use unless you have an eraser that does a good job and doesn’t harm the paper too much

• With your finger - you use your finger as a guide to work your way through the maze and solve it. This method allows multiple people to solve the same maze

• With your eyes - my personal most common maze solving method. Works for most maze types, although you need to add in a more comprehensive method for any spiral maze.

• Reverse fill with a writing utensil - a method I used to use because I liked the way it looked. You use a pen / pencil and start at dead ends, filling each in until you reach a new branch. Eventually this leaves only the correct path NOT filled in, creating a reverse solve !

• Of course online puzzles and mazes will use a combination of arrow keys or your mouse to solve a maze.

2 CHEAT CODES TO SOLVE MAZES

• Solve it in Reverse - if a maze is giving you trouble, try solving it in reverse. Most mazes are mush easier this way since the maker of the maze likely designed it specifically to be solved in the Start to Goal direction. Of course some maze designers take this method into account and design difficulty in both directions ! These are called Dual entrance/exit mazes and you can learn how to make on and see examples of them here.

• Middle Marking - This is what I call it. Before starting the maze pick a central spot in the maze and follow it until you reach a dead end. Color out that dead end. Choose the spot directly to the right of that spot and do the same. Repeat. The goal is to block out one side of the maze as unpassable by cutting it in half. Can also be done north/south. Here is an example where I repeated this 5 times (using 5 different shades of grey) and cut off the bottom half of the maze as a possibility. If I wanted to continue using this method I would start at the northern border and work my way down until I found the passable pathway !

Those are 15 ways to solve a maze. Good luck and happy mazing !

Case Study#6 - How to Improve a Maze - Uxmal

While this particular maze never made my list of abandoned mazes or mazes in need of improvement, in the time between making this maze and posting it on the site I decided to try to improve it. So, now it becomes my 6th case study.

If you want to read the previous 5 case studies:

Case Study#1 - How to Improve a Bad Maze - Tiki Totem Maze

Case Study#2 - How to Improve a Bad Maze - Danzante Conchero Chichimeca Maze

Case Study#3 - How to Improve a Bad Maze - Red Rocks Amphitheatre Maze

Case Study#4 - How to Improve a Bad Maze - The Hollywood Sign

Case Study #5 - How to Improve a Bad Maze - Severance Hall

You might notice that this blog post title dropped the “bad” maze, because in my opinion the original incarnation of the maze was not bad, just less than what it could be.

Let’s look at that maze, also known as the ‘before’. Now, I want to mention that no matter what size screen you are on it will probably not be large enough. I went max detail on this maze and it is meant to be movie poster size. I like how it looks, but it is a bit bland. Can I improve it?

Here are the enhancements I made to improve and finish the maze:

1. Resize - Any re-sizing will help the maze be seen and improve the look on a screen or when printed. Got rid of a lot of the empty space on top and bottom of the maze.

2. Grass added - I added the setting of the building (no more floating !).

3. Sky added - If you add the ground you should add the sky too!

4. Changed the grout and stone colors - The color of the ruins is what you would see if you were standing in front of them. The grout switches from black to light grey and really changes the look.

5. Change arrow colors - The black arrows no longer look good on the grass colored background so I matched them to the new maze color and that meant I should make sure the…..

6. Letter and branding changed - Re-color to match the ruins and look better against the new background.

FINAL THOUGHTS

And now the “After”. Much better maze. Still difficult to see all the detail without printing it out.

I think this is an improvement. What do you think ?