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I remember Kalles Fraktaler wondering if there was a minibrot if he zoomed forever into the HPDZ Buffalo. I have news for you:

I can guarantee you, there are no minibrots, with the exception of certain structures on the needle. I think there's a finite number of those.

Here's why:
The formula for the HPDZ Buffalo is abs(z² - z + z₀.) The highest exponent is two, meaning the fractal technically has a power of two. But the lowest order of zⁿ controls the Minibrots. Here's an example:

If you zoom into the fractal with the formula z = z² + z⁶ + z₀ (a sixth order fractal according to Kalles Fraktaler), you can start moving towards a minibrot at 10^100 zoom level. Because the order is 6, you'd expect the minibrot to be at (10¹⁰⁰)^{1 + 1/(6 - 1)} (or e120), but it is at (10¹⁰⁰)^{1 + 1/(2 - 1)} (or e200).

This (zoom level)^{1 + 1/(n - 1)} formula formula governs the density of Minibrots in an nth order fractal. If the fractal has two or more exponents with addition or subtraction, n is the number of the lowest exponent. In the example, n = 2, since it is the lowest.

If you zoom into a fractal where n = 1.5, the Minibrot is located at (zoom level)^{1 + 1/(1.5 - 1)}, or (zoom level)³.
If you zoom into a fractal where n = 1.2, the Minibrot is located at (zoom level)^{1 + 1/(1.2 - 1)}, or (zoom level)⁶.
If you zoom into a fractal where n = 1.01, the Minibrot is located at (zoom level)^{1 + 1/(1.01 - 1)}, or (zoom level)¹⁰¹.

At n = 1 (since 1 is the lowest order of z in the HPDZ Buffalo), the Minibrot is located at (zoom level)^{1 + 1/(1 - 1)}, or (zoom level)^infinity. Because the power of the zoom level is infinity, you will have to zoom infinitely.

In the same way abs(z² - z + z₀) has n = 1, if you take away the abs, n = 1, since it's the lowest order.

But with a seed value <0.5, 0i> the HPDZ Buffalo do have minibrots.
Unfortunately perturbation breaks and cannot render these correctly, otherwise I would have done many such Movies