On Friday 06 October 2006 11:17, GillesNadeau wrote: hallo giles and russel, how would i get these formulas to work in xfractint ? i have tried various things, tried to patch together a par file but i get error messages that say it does not know the command c or X i assume x/fractint has a few predfined varibles and that X or c may not be part of them ? sammi
Here a version of your formula based on a model of quaternion by Ron Barnett. The conditions of bailouts are different but it is your differently written formula. I hope not to annoy you with that. Said me what think you.
Regard,
Gilles
Neo-T_set2 { cz=pixel, cv=real(p1) z = v = 0
a = z*z - conj(v)*v b = z*v + conj(z)*v z = a +cz v = b +cv (|z|+|v|) < 8 }
----- Original Message ----- From: Russell Walsmith To: Fractint and General Fractals Discussion Sent: Tuesday, October 03, 2006 23:11 Subject: [Fractint] Neo T-set
Fractal Folk,
Pondering how quaternions (q = (n,i,j,k) could be represented by real numbers, I realized that when q is squared the noncommutative elements cancel out: e.g., ij + ji = k - k = 0. Therefore, letting X, Y, V, and W represent the axes corresponding to n, i, j,and k respectively, we can generate a 4D M-set by:
4D M-set { X=real(pixel), Y=imag(pixel), V=real(p1), W=imag(p1) x1 = y1 = v1 = w1 = 0: x2 = x1^2-y1^2-v1^2-w1^2 + X y2 = 2*x1*y1 + Y v2 = 2*x1*v1 + V w2 = 2*x1*w1 + W x1=x2, y1=y2, v1=v2, w1=w2 z = x1^2+y1^2+v1^2+w1^2 z < 16 }
We recall that the M-set generates from real numbers by
2D M-set { X=real(pixel), Y=imag(pixel) x1 = y1 = 0: x2 = x1^2-y1^2 + X y2 = 2*x1*y1 + Y x1=x2, y1=y2 z = x1^2+y1^2 z < 16 }
and interpolate to find
Neo T-set { X=real(pixel), Y=imag(pixel), V=real(p1) x1 = y1 = v1 = 0: x2 = x1^2-y1^2-v1^2 + X y2 = 2*x1*y1 + Y v2 = 2*x1*v1 + V x1=x2, y1=y2, v1=v2 z = x1^2+y1^2+v1^2 z < 8 }
Inserting this last formulation into Gerald D's marvelous 3D T-set formula gives the image at
http://ixitol.com/NeoT-set.GIF
This is evidently a solid of revolution, more or less the image I was expecting to see when we first got on to this "triternion" thing way back when.
A bit rushed at the moment, I'll post some pars later.
Ciao, Russell
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