Fuzzy Graphing Reveals Hidden Mathematical Shadows
The Shadows Lurking in the Equations – Underwater Islands
Conventional graphing shows only exact solutions, but FuzzyGraph visualizes error, exposing invisible features like black holes, shadow lines, and underwater islands. The author demonstrates six examples where non-binary graphing reveals hidden mathematical topography, including near-solutions that can be tweaked to become visible in standard graphs.
These are like underwater islands - underwater mountains that are just below the surface of the water (or in this case, the error == 0 surface).
- wrs
Isn’t the “error in the equation x = 0” just…x?
- MarkLowenstein
My gut tells me that exploring mathematics in this way has very high potential for bringing on future advancements. (1) Simple elements that (2) reveal coherent structures, and were (3) hidden to historic geniuses due to requiring exhaustive computation.
- simojo
These visualizations are cool, but I feel only a little misleading. Any 2D relation can be plotted in 3D, and setting z=0 shows the original line in 2D. The whole notion of fuzzy is really just saying "let's make a heat map of how far z is from 0". That said, I can see how for some people, thinking about the roots of a function in 3D this way _could_ help unlock deeper understanding of where your roots are at than just staring at 3D graph.