s_{0}=1.0, s_{i+1}=(0.8+0.6i)*s_{i}

Center: 0+0i; Zoom = 0.004

Here is the original starting point for this series. The previous formula, , was my intent. I messed up the order of operations in the program code. I have a few images with this formula, and I felt compelled to first show the big picture view.

You may be familiar with the exponent rule (x^{a})^{b} = x^{(ab)}.
The rule works for real numbers, but not for complex numbers. The multi-value nature of complex exponentiation gets in the way. Try x=-i, a=2, b=1/2 as an example.

The image is here only to introduce the formula. It is not very pretty, and I am not going to talk about mathematical significance, so there is nothing more to say.