Fractint stored the fractal parameters in its GIF89a output files, so that if you or someone else loaded them into Fractint later, you could recalculate at a higher resolution, or explore other parts of the fractal, or vary parameters.
Screenshots or PNG files are a common way to share circuit diagrams from circuit simulation programs. What if machine-readable circuit topology information was included in these files? You could take the Fractint approach and just include a special parameter block, but that will be lost if someone, say, crops the image, or uses a screenshot program to get the image, or transcodes it to JPEG. What if you sort of barcode or watermark it in the image itself?
The first circuit given in Level Shifter has 6 components; in the encoding used by Falstad's circuit simulator, it occupies 224 bytes, or 133 bytes gzipped, about 22 bytes per component. I think it's probably possible to beat this by about a factor of 3, about 7 bytes per component, 56 bits per component. Given that each component occupies about 500 pixels it seems like it should be pretty feasible to do this.