The Path Forward

My Current Thoughts Concerning
Unicursal Maze Research

2023-04-28: In a few days, I will be taking an extended break from working on Unicural Mazes for social functions. I shall resume my work by mid-May. I apologize for any inconvenience this may cause visitors. I do intend to "make up" for the lost work so that a normal progression of work may resume, as if no break had occurred at all.

In compensation for this extended break, Exhibit #001 in the gallery shall remain open indefinitely until, at least, the extended break ends. The premiere of Exhibit #003 shall be delayed until after the extended break ends. Thank you for your understanding.

2023-04-15: Finding all of the paths in the latest diagonal unicursal maze original pair took me by surprise. I knew that I was reaching the end but I thought that I had more cycles to go. Just goes to show how easily you can lose track of time.

I only perform one cycle per day when it comes to diagonal paths. Slow? Absolutely, but it's not a critical field of research. There's some amusement in researching it and I'm genuinely curious about the results. I'm not losing any sleep if nothing ever comes of it (after all, I'm only performing one cycle per day).

However, the completion of that original pair also reminds me of a terrible milestone: I started that original pair back when one of our family pets was still alive and who, unfortunately, has since passed. And, sadly, this is not the first time that I have started on some milestone when a family pet was alive and passed before that milestone was achieved.

Actions have consequences and time is not forgiving to anyone for any reason. As I complete milestones in my research, I must constantly remind myself that the passage of time will take us all at some point. How far shall I get before it's my turn? As morbid as such thoughts are, I must think of them nonetheless.

And, maybe, that's why I only do so much research per day -- So that I may enjoy the rest of it on other ventures. As I get older, I am trying to 'stop and smell the roses,' so to speak. Sure, I may not achieve as many milestones as I would like by being 'casual' in my research but what would I be sacrificing if I was slavishly dedicated?

2023-03-26: As I have written before, I only perform so much work in Universal Maze Research per day. Only so many cycles performed in determined fields. Only one cycle in undetermined fields and diagonal fields apiece. Only one original pair discovered. I won't describe my entire daily work load as I have described it before but the work is not extensive. The entire day and night session lasts... An hour? A little more than an hour, depending upon the peculiarities of that particular day? It's not a lot.

"Why don't you do more?" is the inevitable question. And the answer is simple: Because I want to do this EVERY day. And if I want to perform this type of work every day, I have to pare that work down to something that is mentally, emotionally & intellectually feasible. I have been to that 'other side of the coin,' if you will, and that side is not all roses and rainbows. Burning yourself out does not bode well for your progress. Therefore, I have to design a regiment of research that I can perform every day: Rain or snow, cloudy or sunny, good times and bad. I have performed research on days that pets have died. I have performed research on days where I have had really bad headaches and have not otherwise felt physically well. I have performed research on my birthday and on holidays. There have been very, VERY few days for, at least, the past five years where I haven't performed daily research... And, even then, I have quickly made up for it on the very next day.

It would be easy, especially on days where I am enthusiastic, to work a lot harder. However, I know that, if I want to go far, I need to take it slow and steady. Today was a tough day, mentally, to perform the daily research. Tomorrow, I might breeze through it without a thought in the world. That's just how this research is. And, inevitably, I will get there, I will complete fields and make discoveries. This research is a marathon, not a sprint. I've learnt that lesson the hard way.

2023-03-22: Before paths can be created, you have to determine what the original pairs are in a given field. I've just finished the determined 04x09 field earlier today. When will I actually work on that field in terms of path creation? I don't know. Honestly... Maybe never. I'm currently still on 05x06 and, after that is 06x06. Then comes all of the Nx7 fields (02x07, 03x07, etc.) followed by the Nx8 fields... There's 16 whole fields -- not original pairs -- FIELDS, that I would have to complete before I could get to the 04x09 field.

I quickly realized, walking into this research years ago, that I would never reach the end. It's not about reaching 'the end' (which doesn't exist) but how far you are willing to commit. But isn't that the case in all endeavors?

2023-03-15: In two days, I'll be completing the 0506-57 (technically 0506-05J) determined field. The original pairs have been going quick lately; 5 original pairs in 2023 alone so far and it's only mid-March. Will I be able to complete the entire 05x06 field by the end of 2023? It's possible. There are 9 more original pairs after this current one. I have no doubt that some of them will take longer than some of the more recent original pairs.

I don't want to look too far ahead but 06x06 keeps getting closer and closer...

2023-03-12: One question people might have in their minds is 'Why don't you do MORE per day? Why only so many cycles of THIS and so many cycles of THAT?' It's a fair question. The truth is that, at this point, I perform about an hour of maze creation work per day... Every day. That includes days when I'm sad... Days when I'm angry... Days when I'm stressed out... That amount of work is plenty for me and that doesn't include any work involving content presentation; Any work involving this website is counted as 'content presentation.'

Part of the reason why I don't perform hours upon hours of maze creation per day is because, with more work comes the greater possibility of mistakes. Some mistakes are tiny; Others have been far larger. And none of those mistakes are fairly obvious; I currently don't have a lot of methods to double-check my work to see if I've made any errors along the way. Even if you fall off of a very tall cliff, gravity will eventually force you to collide with the ground below. With unicursal maze creation, if you make a mistake, that mistake could linger for years before being discovered... If it's discovered at all. Instead of falling off of a cliff, making a mistake here is the equivalent of floating in space: There's no gravity to assist you in seeing the error of your ways.

Today, I found a tiny mistake while performing analysis of the mazes. Six mazes were mislabeled in the 0505-13 determined field. It wasn't exactly a huge crisis and it was quickly resolved.

Yet the next discovered mistake might be a huge one. I just don't know how extensive the next mistake might be. I have few tools to discover mistakes except for going back and examining them in various ways. Examining prior mazes takes time... Time that, legitimately, could be spent on creating mazes. However, it's important to be accurate and I'd rather be accurate than fast.

There's a reason why I haven't completed the 5x6 determined field yet; Slow and accurate is always better than fast and sloppy. I'm heartened that I haven't seen any errors since I've slowed down my pace but that doesn't mean that I won't find one eventually. I hope that this is the last error out there... But I know that hope needs to be backed up by constant examination and research.

2023-03-07: The first ever exhibit is now on display in the Gallery. While I won't make an announcement here for every exhibit, I thought that it would be noteworthy to mention. Hopefully, this exhibit will be the first for many to come. On current display are examples of different types of Unicursal Mazes for you to enjoy.

2023-03-05: Every path that I create is special. It's like that phrase, "As a parent, I love all of my children equally." Simply because I dwell on one path or a series of paths more than others doesn't discount those other paths in any way.

Just today, while analyzing path 0506-05-33212 (formally titled, "0506-00g-33212," a determined path) in order to catalog it, I stopped for a moment to appreciate it. There's nothing overly unique about that path; It doesn't contain an unusual amount of corners or decision points... It doesn't belong to an original pair that's significant in any unique sort of way.

I was hit with the thought that it has taken me years to be able to draw that particular path. YEARS. Certainly, if I had worked faster, I could have gotten to that path sooner. Yet, speed isn't the point; The point is that, for all that I know, I may have been the first one to have ever drawn it. Certainly, I'm the first one to have drawn all (or, at the very least, most) of it's predecessors.

It's taken a lot to get there... And to where I am now. The 5x6 field has lasted years for me and I'm beginning to reach 'the end.' Granted, I'm not breaking any speed records but the goal is accuracy, not speed. And the goal is self-education, not false records of achievement. I've earned that path through drawing all of the other paths before it... Learning all of the techniques and procedures to draw that path by drawing all of the predecessors. I didn't push some button on a computer and let some computer program draw them out.

I can't predict when I'll finish the 5x6 field (maybe this year but... Who knows?) but, when I do, I'll certainly be a different person than when I started. I appreciate all of the paths that I've drawn.

2023-03-04: I don't have a content creation problem, I have a content presentation problem. I create Unicursal Maze content for about an hour (and, nowadays, longer) every day.

It's been very difficult for me to mentally justify the time to spend taking that content and re-packaging it into a format that's presentable and understandable for someone other than me. First, the mazes themselves are a bit miniscule when it comes to pixel length and width. I've learned that I've had to "upscale" those pictures, both to make them more viewable and more presentable.

It's never easy to admit fault in anything. My interests have a limited audience and my skills at presenting that interest are limited still. But I am learning to adapt, albeit slowly. After all, the website was re-designed...

2023-03-03: I'm always slightly paranoid whenever I encounter original pairs such as #56 (05F) where they don't yield a lot of completed paths. You always wonder whether or not you've missed a decision point somewhere. I haven't discovered a lot of mechanisms for error correction yet. It's a sore topic in my research; If I make a mistake, I may never know about it for years (or even ever) and this is why I go as slow and cautious as I do nowadays. Yes, I've seen some patterns in the data but those patterns don't tell me everything. It's a 'Which came first? The Chicken or the Egg?' scenario - You need the data to make the tools for error correction but, in order to make the data, you need to make few to no errors.

2023-03-02: I don't think original pair #56 (05F) for the 5x6 field is going to yield a lot of completed paths. I've spent two days working on it (14 cycles total) and I'm already yielding completed paths. The sooner that you start getting completed paths, the less completed paths overall from that original pair that you get. I think that I'm going to get less completed paths from #56 than I did from #55. Is that a guarantee? No, but it just feels that way at the moment.

2023-02-25: Welcome to the re-opening of Unicursal Maze Research. I hope that you enjoy your stay.

For returning patrons, you shall obviously note that the decor has changed considerably. It takes great humility in order to admit that my web design skills are quite lacking for the 2020s. The prior web design may have passed muster in the 1990s but, for today's standards, an update was in order. On this occasion, I have borrowed far more than I have invented; The world of web design has since far surpassed my ability to keep up and it's time for me to learn all of the new tricks while borrowing from those who already know them. Your patience is greatly appreciated in the meanwhile.

There are many changes as one may see, too numerous to elaborate on in one post. "The Path Forward," the website's 'blog,' is still here. However, it shall concentrate on what it was always meant to do: Be my way of expressing aspects of Unicursal Maze Research. For those interested in when I achieve completion of some aspect of that research, there is a new page called exactly that: "Achievements."

The Gallery is also as described, being a section where one may view paths of every type, for amusement, education, enjoyment or any other interest.

The Learning Center is where one may learn several aspects of Unicursal Maze Research. Prior patrons will see that the 'Primer' is there with very little change except for, of course, the updated visuals.

Finally, About provides information 'about' the website and other semi-biographical aspects of the website itself. It will also have contact information and a section detailing the occasional technical changes made to the website.

As with all aspects of the Internet, everything on this website is subject to change. However, I think that this current line-up will persist for some time. Again, I thank you for visiting and I hope that you enjoy your time here.

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:

Diagonal Maze

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:

Determined Maze

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.

2021-11-21: 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).