In GIMP I separated the basic areas “Flower” and “Background” of the original photograph to different layers.
Then I used the “newsprint” filter (lines) on both of them seperately. I repeated it for the center of the flower.
In order to keep the paper connected, I had to manually change some of the result. Also some lines were to fine for the laser (or my skills), so I also manually made the lines wider.
To make it look more “organic” and not so technical, I used (also in GIMP) the “Whirl and Pinch” filter on the flower, used the “newsprint” filter again and whirled the result back in the opposite direction.
In order to generate the paths, I used Inkscape. The SVG files from there I used to cut the colored paper.