Going on with my search for formulas here is a basic formula for a double apple manikin:


The parameter delta is necessary because it is a family of double apple manikins.
For positive values of delta is one pair and for negative values another one.

The start value is always s = 1.0.
Delta Positive Double Delta Negative Double Remark
0.1 -0.1 near 0.0 very small
0.5 -0.5 getting bigger
1.0 -1.0 and bigger
2.0 -2.0 getting reasonable
2.5 -2.5 the best positive
3.0 -3.0 the best negative
4.0 -4.0 starting to connect
5.0 -5.0 connecting
8.0 -8.0 getting compact
10.0 -10.0 getting compact will go on

An animation from delta=6.0 to delta=-7.0 shows the fractal set dependent on delta: