-- On Tue, 21 Jan 2003 16:36:20 Morgan L. Owens wrote:
...though I still say TMan and TJul need a little prophylactic code to stop them from spilling out into six dimensions - unless that's desirable; mainly from the line z=z1+z2+z3.
Right on, Morgan, you da Man! That statement and your Hilbert space reference of a while back helped me recall that a metric space of n dimensions is defined when (a^2+b^2+...n^2)^.5 measures the distance from a point in that space to the orgin. Clearly, the appropriate statement is z=(z1^2+z2^2+z3^2)^.5 I tried this in the formulas and it sharpens the images nicely... so much so that the so-called 'TGirl' now looks more like the TMan in drag... (Hey, we knew from the git-go that he might be different...) What to do? I guess we can't very well call him/her/it 'TIt', so it's back to TMan (XAXIS) { c1=real(pixel),c2=imag(pixel)*(0,1),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2+c2,z3=t3+c3 z=(z1^2+z2^2+z3^2)^.5 z < 16 } TJul (XAXIS) {;Try z1=-0.75 z1=real(pixel),z2=imag(pixel)*(0,1),z3=p3: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+p1,z2=t2+p2,z3=t3+p3 z=(z1^2+z2^2+z3^2)^.5 z < 64 } Since you've already summoned the Dobiasovsky genie, Morgan, maybe you can wish him on to these formulas too... BTW, I don't mean to diss your D3Man when I tell you this (he was, after all, a sort of midwife/godfather to TMan), but he's not really based on D3. The reason is that D3, and in fact a dihedral group of any order, is non-Abelian: Therefore, for some term(s) in the number triplet, say j, the outcome of j^2 will not be equal to -j^2. A fractal formula based on D3 will thus require conditional statements in the initialization line... Now at the risk of being reviled by the list members (big deal...), I must admit that I've actually been using Winfract for most of the past 10 years. Indeed, it's only been within the last year or so that I even installed a real DOS version of Fractint, within just the past few months that I've tried diligently to work with it, and within this latest week bygone that I find a bit of a feel for it at last. There are still things I like about Winfract; e.g., with an frm file in a small window, the alt/tab toggle puts it over the image for editing. But every time I ever tried to load an imported par file, this relatively liteweight program simply choked. Eventually I despaired of the effort, flat gave it up. But in this venue (the List), par files fly around like cards at a poker table and if you can't read 'em, Maynerd, it's really hard to stay in the game. So far, in Fractint, I've actually gotten these files to render, but in Lee Skinner's "Fiery Pit' for example, the evidently crucial color info was lost in the shuffle somehow. In general, the process is still far from intuitive... Suggestions anyone? Thanks, Russ _____________________________________________________________ Get 25MB, POP3, Spam Filtering with LYCOS MAIL PLUS for $19.95/year. http://login.mail.lycos.com/brandPage.shtml?pageId=plus&ref=lmtplus