Free run length

Uuhhmmm, for me it was not very intuitive...but I liked it

@Denis Nazin Regarding the demo above, I think we have already discussed it.
https://mekoramaforum.com/threads/fantastic-mekorama.1413/page-5#post-10394

Thank you.

@Labyrenight Oh, I completely forgot that you already did this research! Sorry. But at that moment I understood absolutely nothing. Now I understand why this happens (I hope I wasn’t mistaken!).
Now I can answer your question!!! :
When you place blocks on white space it affects the length of B's free run. Yes, of course, and now I understand why:
For B, next to the stairs into the void, an infinite number of potential routes of movement arise - this greatly reduces the length of B's possible free run. But!! When you place additional blocks on the white field, you thereby limit the number of potential routes that B can take (from the given position where he is).
In this regard, his route increases - because the lower the potential of possible paths for B (from a certain position), the longer his free run.

The most important law that I understood explains everything (I hope I was not mistaken, but this really explains everything logically and at the moment I have no doubt that this is really true!):

The greater the potential set of routes for movement B, the shorter its free run!
The fewer potential opportunities for movement B, the longer his free run!

I hope I explained it clearly and you won’t lose the meaning during translation. Did you understand me? You agree with me?

@delator77 Thank you very VERY much

@Denis Nazin I understand what you explained. However, not all additional blocks in the white area affect B's behavior.
The position and number of blocks added look so random, that I don't know the pattern yet.
What I just found out is that the addition of blocks that can have an effect is on layers one and two.

@Labyrenight I really hope that I understood the basic law correctly. But such small and detailed details that you want to know are already difficult and require very long and labor-intensive tests. This takes a lot of time. I will be very happy for you if you find answers to your questions (and of course I will be very happy if you share the results of your research). But I'm busy with other research right now. "Low ceiling length limit." This is also very interesting and can be used in gameplay for levels. Therefore, I will now publish a new demo. I really hope you find it interesting!

I suspect there is a shortest path searching algorithm at play. Dijkstra's algorithm is mostly used. This maintains a set of shortests paths to all nodes (tiles in the case of mekorama) the algorithm has so far visited. To expand, it will take a path in the set, and check all tiles it can extend to. Obviously accessibility plays a role (same level, block type, stairs etc.). If a potential tile is already visited by a path that is not longer towards that tile, that tile will be ignored as an extension of the path under consideration. Check all accessible tiles, extend all paths, loop over it all again. A few observations about this:

1) This can explode. If a valid path within the level is long, and the void is accessible, all possible paths of that length over the void are also constructed. So, Martin will have some stop criterion on this. Perhaps it stops at a certain number of paths, or after a big number of tiles has been visited by the algoritm.

2) In a grid, many routes are equal in length, and the path becomes arbitrary. This is I think why certain blocks on the void cause no change, and others a big change. All the paths overlap as a tree-like structure. Place a block on what happens to be the end of a path (all surrounding tiles visited by other paths), and there is little change. Place a block on a tile from which many paths branch, and now all paths become totally different.

Just a hypothesis. I wonder whether Martin may have used the A* algorithm. This may reduce the explosive nature of the algorithm.

Path finding is a whole field of study guys!

@Denis Nazin - My first thought of the level was to

Spoiler

block the white space

but my second thought was there is no space to do so. Thinking that you came up with something else, I tried numerous things that all failed. As I mentioned, going to the center to try a new idea was too long. As for your explanations, great that you provided them in great detail, but as I've told you many times before, I don't read then as I want to figure it out myself.

In hindsight, if you would have given more than one block to the white space, then I probably would have got it before reading the hint.

@Block builder This is a wonderful comment from a master and a great explanation! I absolutely agree! I have already taken a photo of the movement diagram B along the grid of cells many times (relative to the frontal view of the level). Now this is especially relevant! I took another photo of the diagram so that your explanation can be clearly seen:

@Labyrenight The diagram clearly shows the tree of routes along which to move B. And it is very clearly visible that:
1) Blocks in red circles greatly interfere with a huge number of routes for B, and accordingly they will greatly affect his behavior!
2) Blocks in blue circles almost do not interfere with B in the dominant majority of routes, and accordingly will not significantly affect his behavior!

@Meko Guy Yes, yes, this is the right solution to the problem! You thought absolutely right at the very beginning! I didn’t make a longer road for R into the void because it greatly simplified the level and then there was no need for timing and the excitement and sporting interest of this short level was lost. That's why I made the route for R very short - to make it more interesting from a gameplay point of view.
Thank you very much! I'm very glad that you played this demo card.