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The Mandelbrot set computation iterates until a certain distance exceeds two. Two is twice the distance of unity for complex numbers. Unity for B_3 numbers is B[{1,1,-2}]. The VectorDistance function in Synergetics coordinates measures the distance by way of nearest neighbors, similar to the "manhattan" distance for perpendicular coordinates. A Mandelbrot-like set is generated in this notebook, iterating until VectorDistance is twice the VectorDistance of unity for B_3 numbers.
The notebook MandelbrotVectorDistance.nb requires two packages, RBFields.m and SynCoordinates.m, that are part of "Buckminster Fuller Notebooks" (item 600).
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