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Oh what a lovely planet



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=16378

A different way of using double 2 angles :

If we get the angle around the 3rd axis giving:

x^2-y^2    2*x*y    ??

And double the angle around the x axis using:

??      y^2-z^2     2*y*z

So if we take 2*x*y as the given "correct" new value for y then we can calculate the new z value such that both angles are maintained :

x^2 -y^2     2*x*y      4*x*y^2*z/(y^2-z^2)

Of course this gives a slight issue when the new angle around the x axis is 90 degrees i.e. when (y^2-z^2) is zero, but in such a case I've simply used 2*y*z as the new z value because in order to maintain the correct magnitude we have to fudge that anyway.

I should add that the pic is from the degree 8 using the given method.