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z=z^2+(.5+i)^2*c

nice :)

however, wouldn't it be better to do multiply it out, to save some time?

And just a guess but if you make it a unit-vector, you'll probably be able to predict the angle the Mset rotates but avoid scaling it down...

Thanks Kram1032,

Truth is i am an absolute beginner with this software and each experiment is to understand how to custom programme it to do what i want, that is plot in a non quaternion way. This may be  fruitless quest but i am going to have fun trying ;D. I do not want yet to programme in c just to repeat the work somebody else has done,and not have the advantages of lighting ,surface plotting etc.

Of course you are right about the computational savings and the programme produces the same image.

Carlton extensions on z= x²-y²+i2xy+c where x and y are polynomial numerals restricted to x =realz, y =imagz at each iteration.

So i imagine this as a sculpting programme where the bailout is the surface sculpting tool and the function determines the points to be sculpted. The iteration searches out the points and brings them to the cutting surface tool. The only thing that i had not got until now is the visualisation of what the finished object looks like. This is what rendering does and it can add ornaments and bells and whistles!

This to me helps somewhat to explain unexpected regions in the 3d renders. They now seem to be artifacts from the renderer rather than effects of the formula. In particular the bat shape seems to show the carlton extensions hiding the expected bulbs as in the 2d version above. The triangle part in front of the mandy is reminiscent of the atan colouring palette mode etc.

I like the way the coloring turned out for this image.

Out of these four images, the two mentioned in the above quote are the ones I found most interesting, especially the latter one.
 

Happy valentines day !

z=1*z^2+0*i^0+1*c^0+0 iteration 8 using generalized colouring and fractal dimension setting. Enjoy valentines day!