Guide to Cczcpaczcp Part 6

Part 6 of this guide deals with powers that have the same sign and, ignoring signs, are two or greater. The formula is:

z_n+1 = c(alpha*z_n^beta + gamma*z_n^delta)

In common with previous parts, the values used for the parameters are chosen such that the critical value (z₀) is 1.

For

alpha = -1.5
beta = 2
gamma = 1
delta = 3

we get

For

alpha = -2
beta = 2
gamma = 1
delta = 4

For

alpha = -2.5
beta = 2
gamma = 1
delta = 5

So, that is how the fractal looks when both powers are positive, now for when both powers are negative.

For

alpha = -1.5
beta = -2
gamma = 1
delta = -3

For

alpha = -2
beta = -2
gamma = 1
delta = -4

For

alpha = -2.5
beta = -2
gamma = 1
delta = -5

This part is only a brief overview of these two forms of this fractal, unlike previous forms there isn’t immediately apparent a relationship between the sum of the powers, (ignoring signs) and the number of the main features, however, if the difference between the powers is 1 then there is only one main feature, if the difference is 2 there are 2 main features and so on. At the moment I don’t have example images to include in this part. Further investigation is required and I may revisit this part of the guide at a later date. The next part will feature non-integer powers, imaginary powers and complex powers.

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