What we provide

We provide non-periodically tileable PBR textures which can avoid periodic repetitions arising from the conventional tiling method. They consist of partial pieces that can be randomly rearranged without introducing any seams, and this randomness makes it possible to tile the plane non-periodically. They can be readily used with Unity, Unreal and Blender.

<Conventional tiling vs Non-periodic tiling>

How it works

Compared to conventional seamless textures, our textures consist of 2 seamless square images instead of 1, per each PBR component, and each of these images consists of 16 pieces. These 32(16 x 2) pieces share 4 horizontal and 4 vertical common edges and can be arranged to tile the plane in various ways different from the original seamless tilings as long as their edges match those of their neighbors.

<an illustrative figure of non-periodically tileable textures>

Now let’s see how they tile an arbitrary-size plane non-periodically, from left to right and top to bottom. (The reference paper: M. F. Cohen, J. Shade, S. Hiller, and O. Deussen. 2003. Wang Tiles for Image and Texture Generation. ACM Transactions on Graphics (TOG), Volume 22, Issue 3, 287-294)

For the first column in the first row, all 32 pieces can be used of course. Then for the rest of the first row or column, pieces must be compatible with their left or top piece and there are always 8 such pieces in these cases. Finally, in the most constrained(and also the most general) case, pieces must comply with both of their left and top piece. In this case, for each of 16(4 x 4) combinations of vertical and horizontal edges, there are always 2 different suitable pieces. So pieces are selected randomly among at least 2 choices at every tiling step and hence results are non-periodic.

The image presented below shows a general tiling step. Either the 10th or 13th piece can be placed at the second column of the second row, as their left and top edges match the left piece’s right edge(sky blue) and the top piece’s bottom edge(lime), respectively.

<a general tiling step>
<a tiling example using all 32 pieces only once>

As an actual example, the conventional seamless image that looks like the “Digital Rain” from the movie “The Matrix” and the non-periodically tileable version of it, which were used in the previous section’s tiling comparison, are shown below.

<the conventional one>

<the non-periodically tileable version of the above>

Both contain very similar content and are seamless, but the latter consists of the 2 images(instead of 1) comprised of the partial pieces(indicated by the gray lines) which can be put together in many different ways.

Placing these pieces according to the tiling example presented earlier gives the following result.

<the tiling result according to the tiling example presented earlier>

Note that the original seamless image pair only contains the following characters: 0, E, H, J, L, P, b, q, r and y, while none of them appears in this one, as they were took apart and reassembled differently. Instead it shows the new characters: 1, 4, 6, 9, A, C, F, T, U and e.(the character-like shapes at the borders are incomplete and should not be considered, because this one is not seamless as opposed to the original one.) It clearly shows that pieces can be rearranged in a completely different way without introducing any seams at their edges.