Well now, I guess it's going on toward three years since I first showed up on this list with the "triternion" concept. The basic idea was that the cyclical group C6 could be configured as a number system based on ordered triplets and then used to generate 3D fractals. I was sure it would work, although I had nothing to show for it at the time, save for a vague formula that generated a nondescript, amorphous blob. Luckily though, Morgan Owens had also contemplated this idea, and he quickly published a formula that generated a fractal even uglier, but yet more complicated, than mine. Then Jim Muth got to tweaking the formulas, creating variants that at last produced some worthwhile images. Lee Skinner took it from there, and came up with a remarkable series of fractals based on Muth's variations, and Jack O'Tradez was inspired by that to produce some compelling animations. There were others, as I recall, who threw in on this; e.g., Gerald K. Dobiasovsky, for one, had some helpful comments and clarifications... The upshot is that there was a wave of creative energy flowing through the list that I was able to surf ashore. That is, I managed to develop a template whereby any finite group, once set up into its table form, could be imported directly into a .frm file. The C6 group appears in the example immediately below: For p1=0 and floating point on, it gives a view of an object I call the TMan, as p1 varies from about -0.6 to 0.3. C6 group{ x=real(pixel), y=imag(pixel), v=p1 x1=x2=y1=y2=v1=v2=0: a1 = x1^2+ x2^2+2*y1*v1+2*y2*v2 a2 = 2*x1*x2+2*y1*v2+2*y2*v1 b1 = 2*x1*y1+2*x2*y2+v1^2+v2^2 b2 = 2*x1*y2+2*x2*y1+2*v1*v2 c1 = 2*x1*v1+2*x2*v2+y1^2+y2^2 c2 = 2*x1*v2+2*x2*v1+2*y1*y2 x1=a1+x, x2=a2-x y1=b1+y, y2=b2-y v1=c1+v, v2=c2-v z = (x1-x2)^2 + (y1-y2)^2+ (v1-v2)^2 z < 1000 } (Where y=real(pixel), v=imag(pixel), x=p1 will change the view to another axis.) This was all well and good, even if it was not at all the form that I had expected the formula to take. Moreover, no one could figure out to view this object in 3D, and so after a while, interest waned. I played around with it intermittently, and found some neat variants, but just the other night the light bulb came on again. I.e., I finally saw that while the multiplication table I had tried to construct originally presents complications, to square a triternion is a simple, special case. Thus I was able to reconfigure the formula to Triternions{ c1=real(pixel), c2=imag(pixel), c3=p1 x=y=v=0: a = x^2+2*y*v b = v^2+2*x*y c = y^2+2*x*v x=a+c1, y=b+c2, v=c+c3 z=x^2+y^2+v^2 z < 1000 } As far as I have determined, save for differences in scale, these two formulas give identical results. After more investigating, I noticed that the orbits screen gives only horizontal lines. Rather odd... anyway, I tried the fmod options, inside and out, and the results are (IMO) spectacular. So I'm sending along some par files that maybe list members will enjoy. PS: Thanks to Tim Wegner for directing me to this list in the first place, and Jonathon Osuch and others who maintian Fractint. PPS: If anyone has a clue as to how the TMan may be rendered in 3D, lemme know... Ciao, Russell --------------------------Start par files-------------------------- AsgardsGate { ; Version 2002 Patchlevel 5 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=dcls10.frm formulaname=Triternions center-mag=-0.250474/-0.242195/3.917342/1/-135.000000000000455/-\ 6.23001650268406593e-013 params=0.5/0/10000/0 float=y inside=fmod proximity=0.25 outside=fmod colors=000JC8I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8\ xu7zz5zz4zz3<4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE6tD6<6>vAIv9Kv9M<3>x\ 7Sy7Uy6Wz6Yz5_<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0\ Xq0`v0d<2>y0fz0gy0h<3>u1m600enG000t1ns1or2q<2>v2u<3>c5dZ6`U6X<2>\ F9LAAG7FO4KW0Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvi\ nvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<3>SCCXCAaB\ 9<3>uA2zA0xA0<12>SA1QA1NA1<3>D92<3>NN7PQ8SU9<3>`fDhrI<3>UnXRm_Nl\ cJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_jFRoNIzb0<2>zz1zzC<2>zzz<3>jqdfo_\ blU<3>Mb8<6>JF8 } TheGrotto { ; Version 2002 Patchlevel 5 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=dcls10.frm formulaname=Triternions center-mag=-0.0578437/-0.374326/11.30119/1/-134.999999999911097/\ -6.50101500410116273e-011 params=0.6/0/10000/0 float=y maxiter=3000 inside=0 outside=fmod colors=000XkG<3>hoAkp8nq6<2>wt1<6>Zf8Vd9SbA<3>DVF<4>CPCCNBCMA<2>\ BI9BH8BH8<3>AE79D6DE6<3>UI9YJAaLBeMCgODjQF<9>tgGuiGvjG<2>ypGzrFz\ rK<3>yufxukxvqwww<3>rhh`F0<2>ZD0YD0WC0<8>N50M40L30<2>I10I10J20<1\ 3>TA2TA2UB2UB2VC2<3>YE3<3>Q82O61M41<3>Q71R81S91fM5<3>iO5jP5kQ6<7\ >YE4WD3UB3S92Q82<3>I10931A00<3>VK0_P0dU0<3>zm0<3>zb0z_0zX0zU0<3>\ `F0UC0O80H40<2>A4773A73C<3>56K47M48O39Q2AS<8>9QaASbATc<3>E`hFbiG\ di<3>JklKmmJkj<8>BSOAQM9OJ<2>6GB5E86G9<9>EWHFYIGZJ<2>JdMKfNLhM<2\ >UkH } Bifrost { ; 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