Resampling techniques can be context-specific (ex:HQ4X for pixel art) and fractals are an interesting context. I can give two points of view on that:
1) If your image is composed of point samples into an infinitely detailed and completely unpredictable equation, then what's between the samples is unknowable. When zooming, you should stick with single-pixel dots and fill in the spaces between with black or a checkerboard or some other way to indicate "unknown".
2) If your equation is understood to demonstrate a significant degree of local similarity (the area between samples usually resembles the surrounding samples) then, yes a Gaussian reconstruction filter is probably more accurate than point sampling for the task of predicting what the area between samples would look like if you took the time to run the fractal equation for real.
1) If your image is composed of point samples into an infinitely detailed and completely unpredictable equation, then what's between the samples is unknowable. When zooming, you should stick with single-pixel dots and fill in the spaces between with black or a checkerboard or some other way to indicate "unknown".
2) If your equation is understood to demonstrate a significant degree of local similarity (the area between samples usually resembles the surrounding samples) then, yes a Gaussian reconstruction filter is probably more accurate than point sampling for the task of predicting what the area between samples would look like if you took the time to run the fractal equation for real.