Do I speak true or am I telling mathematical porkies?

Is this multidimensional view true? Well, if you generate a sequence of adjacent slices of the Mandelbrot Set, you should see some kind of relationship between them. Here's one I did earlier using the dimension pusher feature at Genius level:

(Constructed with the Layer feature of PaintShopPro.)

Same with the Julia Sets. Adjacent pictures will show small changes from one to the other. Similarly, any collection of slices through the Mandelbrot Set should, when set together, show some kind of relationship. Let's choose Real(C) plus B-axis and generate a number of slices at regular intervals along the Imaginary(D) axis. That's the picture of it above.

Look at the model. Does this look like slices through a solid? Sure it does. Like slicing an odd shaped cake one way, we can rebuild the original cake from the slices. To my eye, I have a 3D model with the Real(C), Imaginary(D) and B axes. You see, my collection of 2D slices really do connect together at a higher dimension. And, in theory, we could build any one of the pure 3D faces of this 4D beast.

 

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