Goulet Pen's November 2010 Ink Drop - Part Two

On Thanksgiving I finally finished drawing the line work for my November Ink Drop Maze. It is a simple three page affair using the six different inks which came in the November drop. I'll talk about the performance and qualities of the various inks in a following post. What I want to discuss in this post are the various stages that I go through to create one of these multiple page mazes.

From time to time someone will see me when I'm working on my maze somewhere. I take it with me most places I go so I don't waste the time spent waiting somewhere. Waiting at a train station, airport, doctor's office, or traffic light (just kidding about that one) can be tedious, but if you have something to work on it isn't a waste of time. Just pull out the maze and a fountain pen and get to work.

But that is beside the point, the point is that sometimes a person will see me working on it and ask, “What in blazes are you doing?” I love to explain it to them. It is a book length maze. Yes the whole book is one maze. Once their eyes begin to glaze over I they usually say something like, “I don't know how you can keep track of where it is going. You must be a genius or something.”

That makes me smile, because there is hardly anything in the world more mindless than drawing a maze like this. That is why I'm so good at it. The brain can go into off mode and the hands and eyes keep on going. Or since my brain insists on trying to get some exercise, it can think about something else and I can still be productive. The reason is because I have no idea where the maze is going. There are only two things to keep track of, which I call the “Ins and Outs”. This is a list of where the maze comes into a page and where it goes out. As long as at the end of the drawing there are no left over items in the list, then the maze will be roughly correct.

I say roughly correct because it would take a miracle for there to be a solution to a longer maze without some editing. Both of the big mazes that I have totally finished had some need to have changes made for there to be a solution.

Let me show you what I mean with the November Ink Drop Maze. Here are all three pages of the maze.

Notice that the labels in the exit circles are only penciled in. This is so that I can make changes if I have to.

Now here are the pages printed out on which I found all of the paths from In Node to Out Node. Along the edge of the page I have listed the beginning node and end node of all the connections. A maze is just a Mathematical Graph after all. At some point I may discuss some of that sort of thing, because the power of graph theory is only now beginning to be realized.

Anyhow, here is the graph that represents the maze. Although each of the connecting lines has a little arrow on it which is the symbology of a directed graph, the maze should really be thought of as a simple undirected graph. This is because a person can travel or trace his route either direction. There is a problem with this graph though. The problem is that the end is not connected with the start. Only a very sick person would post a maze with no solution. That is the sort of thing you learn to do in Evil Medical School.

Here is the graph again with changes made. I made one change so that there will be a solution to the maze. Then I made two more changes so that all but one of the nodes will be reachable by some path. The only circle that you cannot reach is 2H. In an ideal world that sort of unreachable node would not exist, but then neither would world hunger. So one node out of twenty-four is node not bad.

I will post the maze for you to test it out as soon as I scan and edit the pages. Tomorrow is a day off for me, but I'll have another page of the big maze for you on Monday.

Jonathan