Alright, I made a plot, and it turned out pretty cool. I had to limit it to something that could be shared, and where you could actually see the detail on a 1080p monitor, so I only did 0-2,000.
Every point represents a combination of apple and banana values where it's possible to choose the right pineapple value where you get close to 4. Specifically, where your difference from 4 is less than one part per million. For some combinations, you can pick either a large (in the 1000s) pineapple value, or a small (in the 100s) value. Separating these plots out, apparently you never get a good solution with a small pineapple value when the apple and banana values are too close.
Wish that's super cool, is definitely got a pattern going on. Looks almost like a fractal or interference. Also cool how you can see the linear area where there's no possible solution for pineapple.
Yeah, I kind of thought it was just going to look like static, but I was curious, and it was actually pretty interesting.
I was skeptical at first, because you can get patterns like that in cases like taking a picture of a computer screen, when the pixel grids don't line up, but I checked it at 0-200, when the data points are much larger than the monitor pixels, and the patterns are still there.
So I plotted the large pineapple solutions in 3d, and all of the points are almost perfectly in a plane, there's not much to see there. There's some asymptotic behavior here that means that at this scale, the large pineapple solution will always be close to 4*(apple+banana).
The small pineapple solutions were a little more interesting. They are in two separate planes on either side of the divide in the middle. You can see them here. I also raised the error tolerance to add more scatter points, and you can see that there are similar patterns here, the solutions are just sparser.
Edit: Here is the two solution sets together, for comparison.
I was gonna plot the (real) solution set to the original when I had some time, assuming the macOS Grapher utility can even compute it. Will try sage or something if that doesn’t work.
Alright, I made a plot, and it turned out pretty cool. I had to limit it to something that could be shared, and where you could actually see the detail on a 1080p monitor, so I only did 0-2,000.
Here's the graphs
Every point represents a combination of apple and banana values where it's possible to choose the right pineapple value where you get close to 4. Specifically, where your difference from 4 is less than one part per million. For some combinations, you can pick either a large (in the 1000s) pineapple value, or a small (in the 100s) value. Separating these plots out, apparently you never get a good solution with a small pineapple value when the apple and banana values are too close.
Wish that's super cool, is definitely got a pattern going on. Looks almost like a fractal or interference. Also cool how you can see the linear area where there's no possible solution for pineapple.
Yeah, I kind of thought it was just going to look like static, but I was curious, and it was actually pretty interesting.
I was skeptical at first, because you can get patterns like that in cases like taking a picture of a computer screen, when the pixel grids don't line up, but I checked it at 0-200, when the data points are much larger than the monitor pixels, and the patterns are still there.
Is there a way for you to do a 3d plot? That might show the trends a bit more clearly
So I plotted the large pineapple solutions in 3d, and all of the points are almost perfectly in a plane, there's not much to see there. There's some asymptotic behavior here that means that at this scale, the large pineapple solution will always be close to 4*(apple+banana).
The small pineapple solutions were a little more interesting. They are in two separate planes on either side of the divide in the middle. You can see them here. I also raised the error tolerance to add more scatter points, and you can see that there are similar patterns here, the solutions are just sparser.
Edit: Here is the two solution sets together, for comparison.
Now I'm interested in what's causing those patterns, neat how is the same on both planes
Diofruitine, lmao gottem
I was gonna plot the (real) solution set to the original when I had some time, assuming the macOS Grapher utility can even compute it. Will try sage or something if that doesn’t work.
I’ll ping ya if it’s not a reply to your post
I'd be interested to see it.