I've done something similar in another project (avatar generator based on username). That code would always use a seed, and generate a new one when none was supplied.

The main issue I see is that all the non-random numbers in the code would need to remain fixed. I love tweaking those to improve the results. The link you'd share would have to be something like /v1/hash, where 'v1' is a folder with the 'frozen' version of the algorithm.

I also think the results would be less random/erratic, and since the images this generates are only around 150 kilobytes, they are also easy to share :).