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The other day a friend asked me what was the formula for the Mandelbox. He knew already about the z²+c 2D set. So I quickly explained him that the formula was about foldings, meaning z would take at each iteration a subsequent value depending on its position to some given planes in the space.

Using a 2D analogy, would there be any way to graphically represent the formula in a software (Mandelbulb3D, Mandelbulber...)?
For example z²+c would be a parabola, the mandelbox would be some segments (linear and hyperbolic if my understanding is correct).

Then it would be possible to graphically "manipulate" the segments and see the impact on the fractal shape.

I know that as this would be a 2D representation, it would not cater for all cases, but that's just an idea.

Thoughts?

This is exactly what I meant It's intersting to notice that the 2 peaks are somehow similar to the Mandelbox shapes themselves.

What about a negative scale mandelbox, how would the curve look like?

Don't you think it would be great to have the ability to insert key points, choose the curve shape or interpolation method, and see the fractal transforming in real time?