Extend { ; z=z^2 +z +c: params=-4/0 function=ident/ident/ident ; As first posted, this turned out be curiously close ; to Club_Lambda (as a formula), so the parameters ; hav changed and the formula has the same result. z=fn1(pixel), c=fn2(pixel), t=|real(P1)|: if(real(P1)<0) temp =fn3(z) else temp =-fn3(z) endif, z=sqr(z) +temp +c LastSqr <= t } Crown_Clubs { ; Same as before, but formula is more flexible, ; and map doesn't suffer unnecessary losses. ; 40.32s/megapixel@350Mhz. reset=2003 type=formula formulafile=extend.par formulaname=extend function=ident/ident/conj center-mag=-0.227724/0.00422066/1.194434/1.0731/-90/-1.233735336114705\ 21e-014 params=3/0 float=y maxiter=255 inside=0 outside=atan invert=0.3835305831122/-0.1/0 viewwindows=0/0/no/1024/1024 colors=@altern.map } comment { Look mom! See first. Snip later. On Sun, 4 Apr 2004, Jim Muth wrote:

On Sun, 4 Apr 2004, I wrote:

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A formula as simple as Z^2+Z+C will merely shift the M-set around, while leaving it otherwise unchanged.

SherLok Merfy replied:

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That puts ears on your traditional snowman, and his feet melt. <snipped>

The ears and melting feet are what happens when Z is initialized to zero.

The instructions did not specify starting zed at zip. If you wanted to try that, then you could use the function. Clearing zed does _not_ make a difference in the shape of the inner set, and I can see why from the equation z=z^2 +z +c. The first iteration will assign zed to what it would be in the classic, so the next iterations will be much the same. The biggest difference is in the shape and extent of the first iteration. (This isn't necessarily the case when the formula has a flip-flop multivibrator (toggle switch) in it, though). Now, it's bad enough that you didn't look before you lept, but the fact that you're arguing this point has "troll" written all over it.

To see the little fellow moved around while remaining otherwise unchanged, set the starting point of Z to -0.5 which is the critical point of the formula Z^2+Z.

What is this point critical for? Is this a constant you get from differentiation? <a href="http://mailman.xmission.com/pipermail/fractint/2004-April/002743.html"

Posting of Div</a> In any case, my "Div" formula has a bit more range for this purpose, at least to my way of thinking. It scales, it rotates, it shifts -- and then it still inverts at zero.

What's mystifying to me is how I managed to perturb the classic with a real three and still come up with an inversion that seems to contain the entire outer set.

The MandelbrotMix4 formula automatically initializes Z to a critical point of the formula being calculated.

I thot you said you weren't a mathematician. I'm no great believer in the automatic calculations. As far as I'm concerned the automatic inversion coordinates in FRACTINT should be redlined for having a poorly documented derivation. Perhaps it's where the mouse was last pointing. The automatic inversion _radius_ usually works, though. <a href="http://mailman.xmission.com/pipermail/fractint/2004-April/002740.html"

Just in case you're having as much trouble reaching my server as I was today.</a><a href="http://ecn.ab.ca/~brewhaha/img/cards/">Just in case you're not and you've got time to download nearly three megabytes.</a>

If you don't know what this brace is for, then you're not a formula parser: }