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I'm actually doing a bit of that already as I have the generated images saved after the app compiles them so that they are not generated after the first time just called. The difference is that I them named after the results not the inputs. So the results still had to be generated each time.
We all learn something from every project, or every upgrade to an existing project.
Trying to optimize your entire application can be tough to do. Take a good look your process flow, break it into components and see how you can optimize things one component at a time starting with the biggest bottleneck.
Edit: Boy, I missed something obvious here ...
The images you're using are tied to the results, which is the correct way of doing it since the color results are predictable and are a significantly smaller number of possibilities as compared to the input combinations. You should continue to handle this the way that you are.
BTW, your site says it could take up to two minutes to calculate the results. That's a long time for a calculation. You may want to look at improving the efficiency of the algorithm you're using.