The intent of this was to create a reasonably durable but flexible sheet, primarily for wearable purposes. Originally, I tried a square grid, but the sheet tended to break along the grid lines. A hex grid was slightly better, but still experienced stress breaks along grid lines.

The irregular hex grid helps distribute the stresses, making it flexible but still reasonably durable. You could, for example, print a wallet in PETG using this pattern, and it would be flexible enough to fit in your back pocket without breaking.

The attached image is a 90mm PETG disc, 2mm thick, with 50% irregularity. It bends easily without experiencing stress breaks.

I've uploaded the 90mm disc, as well as 2 100mm squares, one at 50% irregularity, one at 90%. There's also a 210mm square sheet that would fill a typical print bed, and take about 10 hours to print.

The SCAD code allows for the adjustment of a large number of parameters, if you'd like to experiment. For example, the vertical position of the membrane can be adjusted anywhere between the bottom and top of the print. I placed it in the center to protect it from friction wear.

NOTE: The SCAD code randomizes the hexagon vertices. Every render will generate a new pattern. You can prevent this by adding a seed value to the rands() function if you wish.