We want to animate falling snow flakes in the Solarus game engine framework.


The main screen size is 320x240 (QVGA for those from bygone days), traditionally animated using wrapping tiles.

Let's pick up a 32x24 one, because the dimensions (width && height) of one tile must be multiple of 8 under Solarus.
Put it into motion with 24 frames so the animation can loop at 40_ms delay per frame (slow snow, persistence of vision).
We get a 18.432_kpx animation (32*24*24), tiled 10x10 on the screen as shown hereafter.

One small tile
WxH kpx tiling
32x24
18.432
10x10


Preferring something with less -- if not without -- patterns ?
We could generate a more evenly randomized tile and ...
we would replace patterns with a grid or ...
we should try to make one single 320x240 tile.

One big tile
WxH kpx tiling
320x240
18432
1x1

This tile is 1000 times heavier (320*240*240=18432_kpx).
Too large / too tall for Solarus, which prefers the overall size of tiles sets
to be less than 2048 for compatibility reasons.

So, besides getting rid of patterns, we also need to limit pixels overweight in the process.
The good news is both those goals can be reasonably achieved by superimposing
two differently sized tiles so that they conceal each other's patterns.

Two differently sized tiles
WxH kpx tiling
32x40+40x24
74.24
2x2

Let's begin the off-putting underlying theory detailed explanations with a basic layout of two same size tiles.
Each one has its own patterns, we label them and
When we overlay both, we obtain a new pattern, unrandomly labeled .

1 * tile #1
1 * tile #2
overlay

Not that good once tiled on the screen. We still see patterns.

Tile #1
 Tile #2
 Overlay
WxH kpx tiling
24x24 13.824 13.33x8
WxH kpx tiling
24x24 13.824 13.33x8
WxH kpx tiling
24x24 13.824 13.33x8

If we do the same thing with differently sized tiles as aforementioned, we get something more interesting.
Let's just take a tile of 2 patterns and another one of 3 patterns :

3 * tile #3
2 * tile #4
overlay

The overlay builds a 'meta-tile' comprised of 6 new patterns which then resume their cycling
(lightened part in the above table).
Those 6 patterns are built upon only 5: 2 from tile #3 ( and ) plus 3 from tile #4 (, and ).
Arithmetically, 6=lcm(2,3) and 5=2+3 (arrest this man, he talks in maths).
We do not 'see' 3 repeating or 2 repeating but only one larger .

Tile #3
 Tile #4
 Overlay
WxH kpx tiling
16x24 9.216 20x10
WxH kpx tiling
24x24 13.824 13.33x10
WxH kpx tiling
48x24 23.040 6.66x10

With this second tile example, the meta-tile is 48x24 (from a 16x24 tile and a 24x24 one).
Tiny compared to 320x240 but the bigger the meta-tile, the fewer patterns.
So what would be the best ratio for our screen (smallest tiles for biggest patterns-concealing) ?

That would be scann'd and dimensioj-kalkuli is here to enumerate all the possible combinations;
among which two in particular attract attention.

meta-tile tile set W / H H / W
sizes A 160 1280 40 32
sizes B 120 960 40 24

Since 32 is 1/10 of the screen's width and 24, 1/10 of its height,
let 32 be the width for tile #5 and 24, the height for tile #6.
We get a 160x120 meta-tile. 1/4 of the screen. Shiny.

There is also another scheme: 40x32 + 24x40.
Unfortunately, 40*32*32+24*40*40 = 79.36_kpx when 32*40*40+40*24*24 = 74.24_kpx only !

Now is time for kahelo-animi to (slowly) generate images magically.

Tile #5
 Tile #6
 Overlay
WxH kpx tiling
32x40 51.2 10x6
WxH kpx tiling
40x24 23.04 8x10
WxH kpx tiling
32x40+40x24 74.24 2x2

Compared with the first two one-tile solutions, ≈ lightest * 4 but ≈ heaviest / 250.
Totally worth it, as it prevents eye bleeding. Judge yourself.

One small tile
 Two differently sized tiles
 One big tile
WxH kpx tiling
32x24 18.432 10x10
WxH kpx tiling
32x40+40x24 74.24 2x2
WxH kpx tiling
320x240 18432 1x1

Remains to be applied to Solarus:


My God !
It's full of stars.
And, voila ! solarus-vetero.tiles.png solarus-vetero.dat
Crystal bits of snowflakes all around my head and in the wind.

The scenery provides its own patterns hiding as shown below
(at least if your browser supports the APNG format,
customary animated GIF anywhere else for compatibility).

Foreground flakes
Are sparse, scattered and fast.
Could also be big and bright.
Background flakes
Are numerous, tight and slow.
Could also be tiny and dark.

Of course, the principle is not tied to two tiles top, it would work well with way more.
Needless to say, laziness can grasp even the most motivated ...

Similar to the context-free chaos theory, this method should be quite ecumenical
and could theologically theoretically be applied to animations other than snow: mist, rain, swell ...
It might as well already exists, just like this ancient 'differential scrolling' was indeed a mere parallax.