As this writing is a collection of my ideas that have not been written down before now, this page will be gradually updated and refined whenever I recall more and more of my ideas concerning the topic and feel the want. I will perhaps add more such pleasing patterns, eventually.
I introduce here what I refer to as Pleasing Patterns; I have no better name for these and quite like it by now. It is not uncommon to see a mobile phone with a three by three password mechanism in use. It was 2007 or 2008 when I first saw one of these in use and decided to create my own patterns, including that which I hold most dear. The base of these ideas is clearly not my own, as I did not create this password mechanism, but I have created some pieces I consider beautiful and have also created a format for storing such patterns, which is what is being introduced.
The following is the basic grid for these patterns:
The following is the true grid these images adhere to:
It is clear that the basic form of the grid can be summed in twenty bits, corresponding to each individual line segment being present or not. The true form of the grid merely increases this to thirty six bits. In my original envisioning, this was sufficient. However, I came to value the order of the pattern as being particularly important, enough so to warrant a format that preserved this. This also had the side-effect of forcing the patterns to be contiguous, which is a nice quality to have.
The numerical format for describing these patterns will now be described. Firstly, it is important that there be a mechanism for versioning and whatnot and so the first six bits are to be used for this, with this format being described having all set to zero. Following this will be the number of lines in the pattern, with six bits being sufficient. I do not consider it important to permit an empty such pattern and so the count can be thought of as being incremented, allowing one to sixty four lines. Following that is the starting point of the pattern, which requires four bits, and is described by the first bit indicating the ninth position if set to one and with the following three bits indicating the position otherwise. After this, the format is merely collections of three bits representing the following position from the previous. The following shows the positions of the grid, starting from one rather than zero, as that is more pleasant:
The following positions are ordered in a simple manner: the current position is merely skipped in the counting. Here is the ordering from the center position, the fifth position:
For some history of the format, I prefer to avoid leaving anything that could be considered a hole in my numerical formats and so had a different idea for specifying the starting position. The following depicts one ordering of the grid; another potential ordering has the third and fourth quadrants swapped for a clockwise ordering:
My original thinking was to split the four bit starting position code into two bit segments, with which the first half indicates the quadrant and the second half indicates the position within that quadrant. Expanding this to a table revealed the folly, as the center in particular was able to be specified in four ways whereas many positions had only a single unique specification.
An implementation and other tooling for this format is not yet in a state suitable for the public.
I will now display my pieces. The first is the oldest and is a simple alteration of a basic decimal two:
This is among the first I made and also the most precious to me. I started with a pattern from the center, went up and to the right, and I recall the rest flowing from my hand in such a pleasing way:
This is by far the most recent pattern, but still has a charm to it:
This pattern is also old, but the original was lost, I believe in the fourth quadrant according to the earlier ordering shown, and this is my closest approximation to it: