The Path Forward

2022-05-07: While analyzing DETERMINED 5x5 paths, I noticed that I had made an error in the DETERMINED 5x5 field, original pair #10 (formal designation #01E). The resolution of this error created two more original paths, increasing the total number of original paths for that pair to 28.
Forgive me, Asterion.


2022-05-06: I have completed all of the DETERMINED paths for the 5x6 field, original pair #48 (formal designation #04P). There are 141 original paths in this configuration.
Praise Asterion!


2022-04-06: I have completed all of the DETERMINED paths for the 5x6 field, original pair #47 (formal designation #04L). There are 120 original paths in this configuration.
Praise Asterion!


2022-03-16: I have completed all of the UNDETERMINED paths for the 4x5 field, original starting point #4 (formal designation #00C). There are 117 original paths in this configuration.
Praise Asterion!


2022-03-10: I have completed all of the DETERMINED paths for the 5x6 field, original pair #46 (formal designation #04H). There are 88 original paths in this configuration.
Praise Asterion!


2022-02-18: I have completed all of the DETERMINED paths for the 5x6 field, original pair #45 (formal designation #04F). There are 25 original paths in this configuration.
Praise Asterion!


2022-02-15: While analyzing DETERMINED 5x5 paths, I noticed that I had made an error in the DETERMINED 5x5 field, original pair #07 (formal designation #010). The resolution of this error eliminated an original path, lowering the total number of original paths for that pair to 103.
Forgive me, Asterion.


2022-02-12: I have completed all of the DETERMINED paths for the 5x6 field, original pair #44 (formal designation #04b). There are 35 original paths in this configuration.
Praise Asterion!


2022-02-04: I have completed all of the DETERMINED paths for the 5x6 field, original pair #43 (formal designation #049). There are 24 original paths in this configuration.
Praise Asterion!


2022-01-30: I have completed all of the DETERMINED paths for the 5x6 field, original pair #42 (formal designation #045). There are 45 original paths in this configuration.
Praise Asterion!


2022-01-23: While analyzing DETERMINED 5x5 paths, I noticed that I had made multiple errors in the DETERMINED 5x5 field, original pair #06 (formal designation #00s). The resolution of these errors created two new original paths, raising the total number of original paths for that pair to 58.
Forgive me, Asterion.


2022-01-19: I have completed all of the DETERMINED paths for the 5x6 field, original pair #41 (formal designation #041). There are 38 original paths in this configuration.
Praise Asterion!


2022-01-10: I have completed all of the DETERMINED paths for the 5x6 field, original pair #40 (formal designation #03X). There are 49 original paths in this configuration.
Praise Asterion!


2021-12-31: I have completed all of the DETERMINED paths for the 5x6 field, original pair #39 (formal designation #03T). There are 80 original paths in this configuration.
Praise Asterion!


2021-12-27: While working on drawing LOOPED mazes (Unicursal mazes that may be formed into a loop), I noticed that I had made an error in the DETERMINED 4x5 field, original pair #26 (formal designation #02E). The resolution of this error created a new original path, 0405-26-3334, raising the total number of original paths for that pair to 8.
Forgive me, Asterion.


2021-12-19: PROGRESS.HTM, TERMINOLOGY.HTM pages modified.


2021-12-18: Fun Fact - Did you know that the most original paths for an original pair (so far) is original pair #013 (formal designation #01C) for the 5x6 DETERMINED field. There are 397 original paths for that pair.


2021-12-14: Fun Fact - There are 6 original starting points in an UNDETERMINED 4x5 field.


2021-12-13: Fun Fact - There are 66 original pairs in a DETERMINED 5x6 field.


2021-12-12: I have completed all of the DETERMINED paths for the 5x6 field, original pair #38 (formal designation #03P). There are 88 original paths in this configuration.
Praise Asterion!


2021-12-10: What's a "diagonal" maze? As described earlier, a diagonal maze is a maze where you can travel in eight directions (north, north-east, east, south-east, south, south-west, west, north-west) instead of the usual four (north, south, east, west). When I write "diagonal," I'm referring to a "determined diagonal" maze, since it already has an original start and end point before the path is filled in.

Diagonal mazes have three "degrees" to them. I only concentrate on the "1st degree" which are mazes that have original starting and end pairs that are otherwise 'legal' but are impossible to complete unless a diagonal path is used. Here is an example of one such diagonal maze before it's path is filled in:


2021-12-04: I have completed all of the DIAGONAL paths for the 3x6 field, "1st degree" pair #2. Praise Asterion!

However, in more somber news, I discovered a mistake that I had made in the DETERMINED 4x6 field (original pair #33) while performing my routine tasks. Discovering these mistakes is one of the reasons why I try to go back and analyze prior paths; You never know when you'll find an error.It's never easy to admit fault but, on the bright side, discovering the mistake means a more complete list of completed paths and the discovery of three more unique paths for that pair.


2021-11-30: What's a "determined" (or, as I sometimes call them, pre-determined) maze? It's a maze that already has it's starting point (the solid square) and the ending point (the green cross) already on the field of points before the path begins to be formed. The end of the path, if you will, is pre-determined and, hence, the name. Here is an example of a determined maze yet to have it's path filled in:


2021-11-28: I have completed all of the UNDETERMINED paths for the 4x5 field, original starting point #3 (formal designation #008).
Praise Asterion!


2021-11-25: I have modified the front page to include a picture of a recently completed maze. I hope that displaying these types of paths becomes a regular, almost daily feature. I have also added the "blog" & "primer" pages to the main menu on the left of the index page.


2021-11-23: I have completed all of the DETERMINED paths for the 5x6 field, original pair #37 (formal designation #03L). There are 83 original paths in this configuration.
Praise Asterion!


2021-11-21: All journeys must start somewhere and so it may as well start here. And where is here? 'Here' is this blog, where I will prototype sections of the tutorial as well as comment upon my journey to better understand unicursal mazes. Please do not link to this page for I have no idea for how long it shall remain on the internet or even at this very location.

For my first entry, I may as well tell the readers what exactly I do everyday in terms of unicursal path 'research' (and I do consider my daily work on the topic as 'research').

A lot of this list will contain unfamiliar terminology; As more entries are added, the terminology shall become clearer. I apologize for the initial confusion.

Firstly, I complete anywhere between 1 to 7 cycles of determined (or pre-determined) mazes. Why the range? It has to do with how many cycles there are in a row of seven possible mazes in the directory window on my computer. An illustration would convey this concept far easier but, for now, understand that I go through as many as seven and as little as one cycle per day of this type of unicursal maze.

I then complete 1 cycle of diagonal mazes. A diagonal maze is merely one in which there are eight directions instead of the usual four.

I next complete 1 cycle of undetermined mazes. Ever so briefly, an undetermined maze is one in which there is a starting point but there is no initial end point.

From there, I discover 1 new original pair of starting points and end points. From there, I create a new maze template for the original pair that I have found.

Next, I analyze the number of decision points in a particular location on a given type of maze and write down the results for further analysis (and, yes, I have seen patterns in these results and those patterns are fascinating).

Finally, I analyze up to 3 mazes and write down the statistics of these mazes on a spreadsheet for further analysis. I will admit that I will always be perpetually behind on this task from where I currently am but some progress is always better than none.

All of that activity usually takes anywhere between 30 minutes to an hour each day and, with very rare exception, I have been very consistent in performing these tasks. Even when I have not, I have made up for the activity on the very next day.

However, I typically perform some 'extra-curricular' activities much later on in the evening, sometimes even being the very last tasks that I perform before retiring for the night. These tasks are varied but, to name just a few, I also conduct research into 'loops,' 'obstructions,' 'rules' and administrative tasks surrounding the research. Sometimes, these tasks are performed for only a few minutes while others may exceed for as long as perform the routine daily work).