Rotabulbs

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Offline FractalDave

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« on: October 03, 2018, 12:06:33 PM »
"Rotabulbs" is the name I've come up with for the "bulb" style fractals produced when y,z in (x,y,z) is rotated (say as a complex) around the x-axis, prior to treating as a quaternion with 4th dimension zero in a following function, though more generically we don't necessarily have to stick to 3D or to using quaternionic math in the second part ;)
Here are two images of a Minibrot from such a formula one is just a detailed crop from the large original of the other.
In this case the y,z angle is doubled and in the quaternionic part the angle is tripled but the magnitude only doubled,




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Offline FractalDave

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« Reply #1 on: October 05, 2018, 10:21:20 PM »
Wondered what would happen if (y,z) in (x,y,z) was just rotated by the original angle of (y,z) for the "pixel" (i.e.point in 3D/4D) rather then the changing value, Not really bulbs, but interesting.......these are from 8*original angle for the (y,z) and then a power 8 quaternion.

Offline FractalDave

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« Reply #2 on: October 09, 2018, 01:54:00 PM »
Added the yz rotation scaling as a single function that can be called at the start of each iteration of any 3D/4D formula.

Examples attached are the standard W/N degree 4 with yz angle also scaled by 4 with the magnitude of yz constant and the W/N degree 6 with the yz angle scaled by 6 and the magnitude of yz constant.

Offline FractalDave

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« Reply #3 on: November 13, 2018, 11:54:19 AM »
I'm trying quaternionic style angle scaling (see the "whipped cream on steroids" thread) and now bicomplex angle scaling.

Attached is a part of a standard Mandy q^2+c quaternion but with a plain bicomplex calculation on q first that scales the bicomplex angle by 4 but only squares the power followed by a full bicomplex squaring of jkri (i.e. switch axes order to jkri, raise bicomplex ri/jk to degree 2 and switch back to rijk).