Mandelbrot Set + Symmetry Groups ∗ Higher Dimensions = ?

We construct the MaṇḍalaBeth (higher dimensional analogs of the Mandelbrot set) with various symmetry groups. The generating function of the MaṇḍalaBeth is the sum (over the symmetry group) of conjugates (by isometries) of 2D projections (generating functions of the Mandelbrot set).