Faberge Fractals

What do you get when you mash up fractal with Fabergé egg? This gorgeous fractal art from Tom Beddard of subblue, aptly titled Fabergé Fractals. Simply gorgeous!
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Ah, but something sort of along those lines seems so simple when expressed as a function f:
f(0,X) = X
f(n,X) = f(n-1, "Which came first, the chicken or the X")

Instead, spice it up with function A:
A(0, 0, X) = X
A(0, n, X) = A(0,n-1, "Which came first, the chicken or the X")
A(m, 0, X) = A(m - 1, 1, X)
A(m, n, X) = A(m - 1, A(m, n-1,X), X)

The exercise for the "casual" reader would be to find how many times the word chicken comes up in A(4,3,"or the egg") before you decide you hate math.
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