10 01 00 00 10 11 10 00 00 10 01 01 01 11The program found the following partial patterns when trying to find restrictions on each of the tiles (followed by the tiles that are included and the tiles that are not included in the pattern):

..... 10 01 00 00 10 11 10 ..00. 00 00 10 01 01 01 11 .010. .000. ..... ..... 01 00 00 10 10 11 10 .000. 00 10 01 00 01 01 11 .010. .00.. ..... ........ 01 00 10 10 00 11 10 ......0. 00 10 01 00 01 01 11 ...001.. ..0100.. ..0010.. ..100... .0...... ........ .0.10011001.0... 01 00 11 10 10 00 10 ..0.10011001.0.. 00 10 01 11 00 01 01 ...0.10011001.0.It is obvious that third and fourth pattern can be combined to fill an infinite square tiling, where each horizontal line has the pattern described by (00(11|1))*. Once the fourth pattern is used, these are the only patterns that can be possible, thus excluding the first and second pattern. This proves that this particular square tiling does not have an infinite solution using all possible tiles in the set.

00 10 01 10 01 11 10 00 10 10 01 01 01 11The program found the following partial patterns when trying to find restrictions on each of the tiles:

.00. 00 10 01 10 01 11 10 .00. 00 10 10 01 01 01 11 .00. ..... 10 00 01 10 01 11 10 ..10. 10 00 10 01 01 01 11 .010. ..... ........ 01 10 00 10 01 11 10 .10101.. 10 01 00 10 01 01 11 ..10101. ........ ..... 01 00 10 01 10 11 10 .010. 01 00 10 10 01 01 11 .01.. ..... ........ 01 11 10 00 10 10 01 ...101.. 10 01 11 00 10 01 01 .101101. ..101... ........The first pattern implies that any 0000 tile (where

00 01 00 11 11 10 01 00 00 10 10 01 11 11The program found the following partial patterns when trying to find restrictions on each of the tiles:

.000... 00 01 00 11 11 10 01 ..000.. 00 00 10 10 01 11 11 ...000. .001100... 01 00 11 10 00 11 01 ..001100.. 00 10 01 11 00 10 11 ...001100. ..... 11 11 10 01 00 01 00 .111. 10 01 11 11 00 00 10 .101. .111. .....The combination of the first two patterns implies that only diagonal patterns for the form ((0)*0110)* can occur. These exclude the occurences of the last two pattern. This proves that this particular square tiling does not have an infinite solution using all possible tiles in the set.

00 11 01 11 11 10 01 00 00 10 10 01 11 11The program found the following partial patterns when trying to find restrictions on each of the tiles:

... 00 11 01 11 11 10 01 111 00 00 10 10 01 11 11 000 000 ........ 01 11 10 00 11 11 01 .....11. 10 01 11 00 00 10 11 ...1101. ..1011.. ..1101.. .1011... .11..... ........ ..... 11 11 10 00 11 01 01 .111. 10 01 11 00 00 10 11 .101. .11.. ..... ..... 11 10 01 00 11 01 11 ..11. 01 11 11 00 00 10 10 .101. .111. .....If one wants to extend the first pattern to the top, this is only possible with a row of copies from the fourth pattern. The again results in a horizontal line with 1's. Note that also the third pattern can be used. This means that the first pattern includes the third and fourth pattern, but excludes the second pattern. This proves that this particular square tiling does not have an infinite solution using all possible tiles in the set.

00 01 00 01 11 11 10 01 00 00 10 10 10 01 11 11The program found the following partial patterns when trying to find restrictions on each of the tiles:

.000... 00 01 00 01 11 11 10 01 ..000.. 00 00 10 10 10 01 11 11 ...000. .00110... 01 11 10 00 00 01 11 01 ..00110.. 00 01 11 00 10 10 10 11 ...00110. ...... 01 11 10 00 01 00 11 01 ..110. 10 01 11 00 00 10 10 11 .1011. .1101. .011.. ...... ..... 11 11 10 00 01 00 01 01 .111. 10 01 11 00 00 10 10 11 .101. .11.. ..... ..... 11 10 01 00 01 00 01 11 ..11. 01 11 11 00 00 10 10 10 .101. .111. .....This square tile is much like third square tile. The combination of the first three patterns implies that only diagonal patterns for the form ((0)*011)* can occur. These exclude the occurences of the last two pattern. This proves that this particular square tiling does not have an infinite solution using all possible tiles in the set.

00 10 01 11 01 11 10 01 00 10 10 10 01 01 11 11The program found the following partial patterns when trying to find restrictions on each of the tiles:

.00. 00 10 01 11 01 11 10 01 .00. 00 10 10 10 01 01 11 11 .00. .... 10 00 01 11 01 11 10 01 .10. 10 00 10 10 01 01 11 11 .10. .1.. ........ 01 11 10 00 10 11 01 01 ......1. 10 01 11 00 10 10 01 11 ....101. ..1011.. ..1101.. .101.... .1...... ........ ..... 11 11 00 10 01 01 10 01 .111. 10 01 00 10 10 01 11 11 .101. .1... ..... .... 01 00 10 01 11 11 10 01 ..1. 01 00 10 10 10 01 11 11 .01. .01. .... ..... 10 01 00 10 01 11 01 11 ...1. 11 11 00 10 10 10 01 01 .101. .111. .....The first pattern implies that any 0000 tile occurs as part of a vertical bar. This also means that if one places a 0 anywhere besides such a vertical bar, that vertical line will also be filled with 0's. If a 1 is placed to the right (or similar to the left) this results in a vertical line with 1's. Besides this line there can be a vertical line with 0's, or a line with 0's en 1's using the second, the fourth, the fifth, and the sixth pattern. But in that case, the next vertical line will be filled with 1's. This exclused the third pattern. This proves that this particular square tiling does not have an infinite solution using all possible tiles in the set.

00 01 11 00 10 11 01 00 11 00 00 00 10 10 10 01 11 11The program found the following partial patterns when trying to find restrictions on each of the tiles:

.011 01 11 01 11 00 00 10 11 00 .011 01 11 01 11 00 00 10 11 00 .000 .... .... 00 10 00 11 00 01 11 11 01 000. 10 10 11 11 00 00 00 10 01 110. 110. .... 00 11 10 11 01 00 01 00 11 .111 00 00 10 10 00 10 01 11 11 .100 .100(The patterns are a subset of the patterns of tenth square tile). The first two patterns can occur in combination, but not in combination with the third pattern. This proves that this particular square tiling does not have an infinite solution using all possible tiles in the set.

00 10 01 11 00 01 11 01 00 11 00 00 00 00 10 10 10 01 11 11The program found the following partial patterns when trying to find restrictions on each of the tiles:

.011. 01 01 11 00 10 11 00 01 11 00 .01.. 00 01 11 00 00 00 10 10 10 11 .000. ..... ..... 11 00 10 01 00 01 11 01 00 11 .11.. 00 00 00 00 10 10 10 01 11 11 .000. ..... ..... 10 00 00 00 01 11 01 11 01 11 0000. 00 10 11 00 00 00 10 10 01 11 1110. ..00. ..... ..0111. 00 10 01 01 00 11 01 11 00 11 ..011.. 00 00 10 01 11 11 00 00 10 10 0001... 11100.. ..000.. ....... ..... 00 10 11 01 11 00 01 01 00 11 .11.. 00 00 10 00 00 10 10 01 11 11 .100. .000. .....The first and the fourth pattern exclude each other. They both need to be included, but because they both have the same triangle filled, they can be placed in such a manner that they must overlap. This proves that this particular square tiling does not have an infinite solution using all possible tiles in the set.

00 10 11 00 10 00 01 11 10 11 00 00 00 10 10 01 01 01 11 11The program found the following partial patterns when trying to find restrictions on each of the tiles:

11.... 10 11 11 00 00 10 00 01 11 10 111.0. 00 00 11 00 10 10 01 01 01 11 11110. 00000. ...... .... 10 00 10 11 00 00 01 11 10 11 ..0. 10 00 00 00 10 01 01 01 11 11 .10. .10. .... ..... 00 00 01 00 10 11 10 11 10 11 .000. 10 01 01 00 00 00 10 01 11 11 .010. .01.. 11.. 11 01 11 11 00 10 00 10 00 10 111. 00 01 01 11 00 00 10 10 01 11 001. .01. ..... 00 00 10 10 11 10 00 01 11 11 ..00. 00 10 11 00 00 10 01 01 01 11 .100. .110. .....The first and the fourth pattern exclude each other, for the same reason as the previous square tile. This proves that this particular square tiling does not have an infinite solution using all possible tiles in the set.

00 10 11 10 00 01 11 00 10 11 00 00 00 10 01 01 01 11 11 11The program found the following partial patterns when trying to find restrictions on each of the tiles:

110. 10 11 10 11 00 00 01 11 00 10 110. 00 00 10 11 00 01 01 01 11 11 000. .... .... 00 01 00 11 00 10 11 10 11 10 .000 01 01 11 11 00 00 00 10 01 11 .011 .011 .... 00 11 01 11 10 10 00 00 10 11 111. 00 00 01 01 00 10 01 11 11 11 001. 001. .100 00 10 00 10 10 11 00 01 11 11 .100 00 10 11 11 00 00 01 01 01 11 .111 ....The first two patterns can be combined and the last two patterns can be combined, but it is not possible combine all four. This proves that this particular square tiling does not have an infinite solution using all possible tiles in the set.