Are the Mandelbrot Cardoids in fact loose form each other?

[kek]

I was wondering do the curves in the mandelbrot-set ever reach each other? And if they do at wich iteration-point at wich scale?

[lkmitch]

I believe that they are tangent to each other and only touch at the infinity iteration.

[kek]

Is there any way to prove it? And would they all touch at same infinity of iterations?

[David Makin]

Is there any way to prove it? And would they all touch at same infinity of iterations?

I don't think you could "globally" prove it, but anything's possible
and
Yes in the sense that for all such points it would take infinite iterations to confirm that they are such a point - of course it would also require infinite mathematical accuracy/resolution.

It should also be noted that *all* inside points on the boundary of the full inside i.e. effectively all the true Mandelbrot (boundary) Set are in fact such points, the problem is that some of the bulbs/cardioids they are part (the edge) of are also infinitely small.