I have a tessellation piece (shown below). I want to use this piece and create a tessellation of a certain amount of pieces so I can laser cut them out of a piece of wood.
You could use this method in Illustrator:
- create a shape like this with your symbol
- Crop the selected area.
- select your croped object and go to Pattern Options (Window>Pattern Options)
once the Pattern option tab opens up click the waffle and select Make Pattern
- A windows will pop up where you can navigate how the pattern should flow, also you can make the changes while preview the pattern.
Once you happy with all the alignments, on the top left corner press Done ( This will save your patter in the Swatches tab)
After all this you can select any shape tool and use the swatch to put in your pattern. Once thats done you have to Expand it by Selecting the object and
select a Rectangle tool (Press M)
Create the shape you want it to be cropped. Make sure the shape has no stroke.
Select all layers and in Pathfinder (Windows>PathFinder) click the crop button.
Hope it was helpful
Use Vector Graphics Software
The important part of the question is the fact that it is going to be used for laser cutting.
For laser cutting you will want your paths to be very precise. From looking at the image you posted, you should probably completely redraw the shapes as vector paths.
Don't overlap paths
Another thing to keep in mind when laser cutting is that the laser cutter will cut any paths you give it. So if you have overlapping paths - like in the tessellation you posted - the machine will make the cut for each path. This can easily end up costing you a lot of money if you're doing this in volume and can also (depending on the material) damage the material. It can also result in incorrect cut thickness (knows as kerf).
The kerf is especially something you want to keep in mind when creating your shapes and choosing materials if you are planning on piecing these shapes back together after they have been cut.
There are a lot of other things to take in to account when laser cutting but that should give you an idea of where to start.