Which antiderivative of what?

It is the 8th indefinite integral of z^2 + c. The equation, in Matlab syntax, is:
    z= z.^8/20160 + z.^6/720 + z.^5/120 + z.^4/24 + z.^3/6 + z.^2/2 +c.*z + c;
I used 50 iterations, and also increased the upper bound (infinity) from 2 to 50.

A few things I don't understand:

Why is it called the 8th? You need 6 repeated integrations to get from z^2 to z^8.

The indefinite integral of z^2+c is 1/3*z^3+c*z + some constant d. Integrating this repeatedly until the degree is 8 should give rise to monomials with a variable in the coefficient (c,d and the subsequent ones), there should especially be a c*z^6*some number. The repeated derivative of your formula goes down to z^2+1 and not z^2+c, however.

Which critical point(s) are you analyzing to get your images? (I find these types of polynomials quite complicated as the cps are dependent on c).

@mcneils:
I explored higher degree polynomials once, but the dimensionality of the parameter space went up too fast - and I usually start with brute force walks. Making the coefficients correlated to one another by using your integration idea would have been an interesting means (but I haven't thought of that back then).

Have you explöred Julia sets with your polynomial as well and found appealing shapes?