Considering the classification on the classification page, z2+c is like a basic formula for Mandelbrot like sets.
As I want to show here:
z + 1/z + c is the basic formula for Beads, Novae and Amoebae.
Unless a scaling factor, a basic Bead, a basic Nova and a basic Amoeba belong to one and the same formula: z + 1/z + c.
This scaling behaviour can be shown for other Beads-, Novae- and Amoebae formulas, too.
So to say this scaling behaviour is typical for Beads, Novae and Amoebae.
| Formula f(z,c) | Start value -1 | Start value 1 | Remark |
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the formula with start value -1 and 1 results in a Bead |
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the formula scaled with 0.8 results in a Nova |
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the formula scaled with -0.8 results in an Amoeba |
Here is an animation showing the scaling behaviour of z + 1/z + c: