I did this pattern before as one of my first stabs at cutting veneer with my laser. This time I was going to better document the process and instead of an experiment, I actually had a plan! (sort of).

I've always liked this pattern, From a technical perspective, best thing is all cuts are straight and square. Worst thing is all cuts must be straight and square 🤔

A little off on either, and gaps will form and propagate throughout the design.
Before I tried laser cutting, I'd use a cheap veneer saw and Exacto knife for straight and clean edges. I did ok, but the knife tends to follow the grain and my saw sucked. Plenty of age old techniques and skill required for even this simple-seeming task, something that people like Paul {shipwright) have long ago mastered but not me.

In comes the laser. Burn the buggers out!
Where a good knife will leave a clean edge and with a slight taper, a perfect gap-free fit, the laser will leave a gap due to the beam kerf and a charred edge.
Several things can be done to minimize those "features"

The Laser

I have a 10 Watt optical power diode laser (my first). Typical hobby grade unit. To use one, good software that goes far beyond anything delivered with the device is required. At this time, LightBurn is at the top of the heap. Really lets you get the most out of the tool for a cheap price.

My setup is a swing down table in my spray booth. Ventilation and compressed air are already there so a perfect place to work.

This is the Ortur Laser Master 3 (LM3), a typical gantry style with a 400mm x 400mm workspace.
One can go nuts with setup. Since I also use this space for finishing, the table gets folded down and the laser set aside. I placed 3/8" steel pins to replace the feet in the corners of the frame. Matching holes in the table top allow it to be securely located in the exact same location when setting up. A backer (spoil) board from a scrap section of Hardie siding (cement based) keeps the laser beam from cutting a hole back to China in the table top. I burned a layout grid on it's top so I know where to place things to cut/etch, even if it's been months between uses. You can see the wood blocks used to align this spoil board to the table.
On top of that, to hold the stuff being cut I use a piece of fluted glass I had. The peaks hold the veneer while the flutes let the smoke escape from below.

There are lots of other ways to get a working setup, this is what I had handy.

Air Assist

The laser head has internal fans to keep it cool, but when lasing most materials soot and smoke will be created. There also is an advantage to blowing air into the cut to clear away burned crud.

Most of the lasers will route this airflow through a "funnel" that also surrounds the laser lens, this airflow will help keep the smoke and soot off of the lens. If anything builds up on the lens, the beam will begin cutting your lens and quickly trash it.

Not much air is needed, even a good aquarium pump will do. I found a cheap airflow regulator so I can record exactly what I use for each material. The key is airflow, not air pressure since if you change a hose the pressure will also change, but if you just keep the airflow constant, you'll get the same results at the laser.

Mounted in an old cigar box with a slip in lid that makes for easy removal if I need to. Measurement is in Liters/minute (Litres/minute for y'all across the ponds 😬)

Anyhoo, onto the project in part 2