I have made a Mandelbrot fractal generator (who hasn't, I know) which can render directly to disk to generate huge fractals.
My first test was a UHD 4k resolution which turned out great (8-bit colour for all of these examples). So I decided to go a little crazy and went 10x bigger in both dimensions, i.e. 38400 x 21600. The resulting file doesn't appear valid in that Photoshop can't open it but even looking at the file properties in Windows Explorer shows that the dimensions/etc are missing.
I thought there was a chance that the limits were 32768 so I tried to go just under that by doing a 30000 x 30000. This still seems to be invalid.
Going down to 10000 x 10000 works fine so I am wondering what the limitations are of the file format?
File size shouldn't be an issue as even the 10x4k resolution file was under 1GB.
It looks the maximum size of BMP can be 32Kx32K and 2Gx2G pixels. Here is the link I found.. http://www.fileformat.info/format/bmp/egff.htm