Y^4 = 0 not being graphed

When inputting y^3 = 0 into desmos, it seems to graph it fine, but for y^4 = 0 there is no graph drawn. This seems to happen for other values including decimals like 0.5. But I would expect y^a = 0 to look the same for every a>0

Thanks for reaching out about this issue.

Our implicit plotter works by taking your f(x,y) and sampling—and recursively subsampling—many points in the plane in an attempt to approximate the boundary between regions where it is positive and where it is negative, because this boundary forms the solution set. But in order to reliably detect that, we need your function to actually change signs at that boundary. Or, equivalently, we need that surface to properly intersect the plane at z=0 , not simply become tangent to it. As a consequence of this, we will never shade a region based on an implicit equation . If an implicit equation (not inequality) is 0 over some region , it means that region is tangent to the plane.

We do this because it’s not feasible to sample every single point in the viewport and check for exact equality with 0 without being intolerably slow. And even if we could, we’d end up plotting a pretty janky boundary almost all the time, because those comparisons would be very numerically unstable due to floating-point rounding error.

This is one of n compromises we make in numerical systems, where n is large.