This page displays a different fractal snowflake for each day of the week.
(The date on your computer must be properly set.) It is possible to download the images individually.
Tremendously improved results are possible by using a true hexagonal grid, that is shifting alternate rows by half a cell.
It is then necessary to use a slightly different digital filter for alternate rows.
You may want to come back to this page in a few months time.
John Conway's game of life can also provide fractal snowflakes, that is, hexagonal fractals. It only takes to use an hexagonal mask, such as the following:
| 0 | 1 | 0 | 1 | 0 |
| 1 | 0 | x | 0 | 1 |
| 0 | 1 | 0 | 1 | 0 |
Each cell is replaced by a weighted sum of the neighbouring cells: The central cell may, or may not, contribute to the result. The usual precautions of not overwriting pixel values before they have been used in all calculations involved, must be taken. The life of each cell is 4 generations, though there is no reason, in principle, for cells not to live for anything between 1 cycle and forever.
It is necessary to save some time when the number of pixels becomes very large; exploiting symmetry can be one solution.It is also possible to remove the problem by evaluating cells only within an evergrowing rectangle centered on the seed; empty cells clearly do not give rise to crystal growth.
The fact that a perfect hexagon is not being employed can be hopefully lost on the viewer by using a rectangular, rather than square, grid. The asymmetries which would have been introduced by the edges of the grid in an hexagonal pattern are avoided by using a comfortably large grid.
I will thoroughly milk this topic by showing 3- D automata in the distant future! It will then make a lot of sense temporarily to store (and shift) local cell values, rather than access array elements a further two times, for adjacent cells.