I'm a real math newbie (I'm an English graduate; please be gentle). I'm building a webapp which allows users to manipulate an image, a little like Photoshop. The app needs to swap out the base image with a pre-rendered one depending on what settings the user chooses.
Currently we're trying to figure out how many editing controls there can be without having to create an infinite number of images. Right now I've been thinking of seven controls, eg:
- Exposure
- Noise
- Pressure
- (etc)
Even a rank amateur like me can see that seven of these fields will produce many permutations: at the moment I'm thinking of them as being binary inputs, eg. Exposure can either be on or off (therefore producing two distinct images), as opposed to a scale (eg. Exposure: 2, Noise: 4 etc).
With 7 field options, each with two states, that's 14 sample points in the set and 7 sample points in each permutation, right? I've been using this tool to help me wrap my head around the problem – it's saying there are 3432 combinations (or 17,297,280 permutations... yikes). Am I calculating this properly?
Alternatively, reading this question, it feels simpler. If I represent my switches like so:
Exposure 0 1
Noise 0 0
Pressure 0 0
XQ Mix 0 0
Invert 0 0
Desaturate 0 0
Equalise 0 0 ... etc
... then in effect I'm generating 7 digit numbers with 2 different possible values ($0$ and $1$) per digit, eg. $2^7$ (128 possible images). Is this right, or is my above methodology correct?
