July 2003 - Fractint - mailman.xmission.com

The "bug "is not a bug!!! Is not! Is not!
by Tim Wegner 26 Sep '03

26 Sep '03

OK folks, listen up. :-) For you Fractint is a fractal program, for me it is the World's Best Quick And Dirty Reference to Complex Transcendental Functions. Press F1, go to "Fractals and the PC", and navigate down to trig identities. I put these in the help because I went through a LOT of books finding these and wanted to collect them all in one place in order to code them up. Some books are too simple and so don't have the formulas, and other more advanced books are too abstract and so don't have them either. The formula for the complex power is as follows: z^w = e^(w*log(z)) (here"^" is ASCII text shorthand for exponentiation, in this case z^w means "raise the complex number z to the power of the complex number w") where: e^(x+iy) = (e^x) (cos(y) + i sin(y)) and log(x+iy) = (1/2)log(x^2 + y^2) + i(atan(y/x) + 2kPi) for k = 0, -1, 1, -2, 2, ... (The log function refers to log base e, or ln. The expression atan(y/x) is an angle between -pi and pi in the quadrant containing (x,y) implemented in C as the atan2() function.) The point of these formulae from a programmer's perspective is that they define the complex valued power function in terms of the real versions of e^x, log(x), sin(x), and cos(x) that are available to the C programmer. The interesting and important thing here is that the value of the complex log is not unique. There are infinitely many different values, with the imaginary members. Put another way: the complex log is not single valued. Let's look at the log. In the "bug" illustration, the complex argument is: (-5.0, 0.0) The assembler log function gives: (1.6094379124341,-3.141592653589793) Coding by hand in C gives: (1.6094379124341, 3.141592653589793) BOTH ANSWERS ARE RIGHT!!! The imaginary parts differ by 2*PI, which is acceptable. What actually causes this is that the log implementation normalizes the result to a particular 2*PI segment. Jim's fatal mistake was when he assumed that given a = 1, b = -5, g = 1, h = -1, j = 1/6, that (-a*b*g*h) is -5. Yes, it's very close to -5 in the actual computer calculation, but "close" wins only in horseshoes. The problem is that the complex logarithm of (-5,0) has an imaginary part exactly on the logarithm software implementation's boundary of 2*PI normalization (namely PI). So if the calculation (-a*b*g*h) drops a bit here or adds a bit there, even a bit of the lowest significance, it can change the imaginary component from ~ PI to ~ -PI. I leave it to the reader to plug both these logarithm values into the rest of the formula for the exponential power, and see that the result is (1.132467200411351, -0.653830243005915) in the one case and (1.132467200411351,+0.653830243005915) in the other, as Jim discovered. Here's the main point - a recurring theme in trying to create fractals with complex transcendental functions. The complex power function x^y is discontinuous because of the ambiguity in the many- valued complex log. Each decision to normalize the log to a particular 2*PI interval in an effort to define a single-valued function creates a discontinuous tear in the result in a different way. The "bug" Jim found had values right on the boundary of the tear, so that tiny perturbations and rearrangements of the code pushed the calculation over the edge of the discontinuity. Fractint is cleared of the unjust accusation! The verdict: INNOCENT! All is well with the fractal world :-) One single absolute truth of the universe is thus upheld again. It is this: There are NO software bugs, ONLY USER ERRORS!!! (Sorry Jim ... -no, not *really* sorry, I lied :-) I suggest the future Fractal of the Day explore a fractal based on a discontinuous complex transcendental function in such a way that the fractal itself has visually manifest tears. There are several examples in Fractal Creations, and I am sure many of the artists here, including the honorable Mr. Muth, know of or can discover examples. Tim Wegner

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Shear Amazement
by Russell Walsmith 02 Aug '03

02 Aug '03

In a recent perusal of Bradley Beacham's "AN INTRODUCTION TO THE FRACTINT FORMULA PARSER" (the FRMTUTOR.TXT file in Fractint) I came across the 'fibo-A' formula. This .frm introduces Fibonacci-type recursions to the Mset formula, and it inspired me to investigate this idea further. I thus came up with the 'Fibrot' formula, presented (in a generalized version) below: ------------------------------parfile----------------------------- Nautiloid { ; July 23, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=Fibrot1 passes=3 center-mag=-6.42033/2.44459/0.04984424 params=-5/-1/1/0 float=y maxiter=300 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } ------------------------------frmfile----------------------------- frm:Fibrot1 { z = 0, c = pixel, j=0, k=1: a = p2*j + p1*k j = k k = a z = z^k + c z < 1000 } -------------------------------endpar----------------------------- Soon thereafter, Jack O'TradeZ used this .frm to render the 'Mosaic' viddie now playing at: http://www.sonic.net/~jot/ufvp.html Both the 'stills' and the video demonstrate that complex parameter values in 'Fibrot' induce a shear factor along the real axis that warps circular shapes into nautiloids. It occurred to me that a variant formula might give more insight into this effect, and this led to a series of 'Nautibrot' formulas, some of which are presented below: ------------------------------parfile----------------------------- Nautilii { ; July 23, '03 ; Version 2002 Patchlevel 5 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=Nautibrot2 passes=3 center-mag=-6.84262/0/0.04783259 params=5/1 float=y maxiter=300 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } ------------------------------frmfile----------------------------- frm:Nautibrot2 { z = 0, c = pixel, k=1, j=-1: j=j*(-1) k=p1*k*j z = z^k + c z < 1000 } -------------------------------endpar----------------------------- Another variant introduces i-axis shear: ------------------------------parfile----------------------------- ShearMadness { ; July 23, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=Nautibrot3 passes=3 center-mag=0/0/0.6666667 params=-1/1 float=y maxiter=300 colors=00000j0j0jj0j00j0j0jjkkkkrkdmwW000W0WW000WW0W0WWFNF<4>rNF\ zNFFVF<4>rVFzVFFbF<4>rbFzbFFjF<4>rjFzjFFrF<4>rrFzrFFzF<4>rzFzzFF\ FN<4>rFNzFNFNN<4>rNNzNNFVN<4>rVNzVNFbN<4>rbNzbNFjN<4>rjNzjNFrN<4\ >rrNzrNFzN<4>rzNzzNFFV<4>rFVzFVFNV<4>rNVzNVFVV<4>rVVzVVFbV<4>rbV\ zbVFjV<4>rjVzjVFrV<4>rrVzrVFzV<4>rzVzzVFFb<4>rFbzFbFNb<4>rNbzNbF\ Vb<4>rVbzVbFbb<4>rbbzbbFjb<4>rjbzjbFrb<4>rrbzrbFzb<4>rzbzzbFFj<4\ >rFjzFjFNj<4>rNjzNjFVj<4>rVjzVjFbj<4>rbjzbjFjj<4>rjjzjjFrj<4>rrj\ zywccdWWWz000z0zz000zz0z0zzzzz } ------------------------------frmfile----------------------------- frm:Nautibrot3 { z = 0, c = pixel, k=1: k=p1*conj(k) z = z^k + c z < 1000 } -------------------------------endpar----------------------------- Finally, in these "Not-a-Brot" calculations, 2 + 3 = 4: ------------------------------parfile----------------------------- L'escagot { ; July 23, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=Nautibrot4 passes=3 center-mag=-0.58651/0.281617/0.6666667 params=4/1 float=y maxiter=300 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } ------------------------------frmfile----------------------------- frm:Nautibrot4 { z = 0, c = pixel, k=1, j=-1: j=j*(-1) k=p1*conj(k)*j z = z^k + c z < 1000 } -------------------------------endpar----------------------------- A generalized nautibrot is: ------------------------------frmfile----------------------------- Nautibrot5 { z = 0, c = pixel, k=p2: k=p1*fn1(k) z = z^k + c z < 1000 } -------------------------------endpar----------------------------- That's about the gist of it... I suspect that these efforts haven't been all for 'naut', for there are perhaps many other patterns that will emerge in this context. I hope that list members will find something of interest here, but hey, it got me all in a state of sheer amazement and that's the bottom line... Ciao, Russell (PS: I think I have this .par file thing down, but if they fail to render correctly,lemme know.)

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Re: L'Escargot
by JackOTradez 02 Aug '03

02 Aug '03

Yea - I figured the typo. It does look like a snail. Those weird people across the pond actually eat the disgusting things - raw! BTW, I have just animated the L'Escargot (Nautibrot4) over 3000 frames at 1024x768, set to the tune "Green Onions", by Booker-T & MG's (anyone remember that one?). In-f'n-credible! Russ - you are not posting your files correctly. Those (like me) who know the rite way can fix it, but others may have a problem, and will not see your fantastic images. In the PAR, there is a line like "formulafile=next.frm". It is wrong. Instead of "next" you should have the name of the specific formula, in this case "Nautibrot4". These images are incredible - how do you find these things??? I will now try to animate Cornucopia; me and ((( 5^(1/2)) + 1) / 2 ) "Golden Ratio" go back a long way . . .. ... ..... ........ Stay Amazed, JoTz

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Re: [Fractint] Shear Amazement
by Russell Walsmith 31 Jul '03

31 Jul '03

The nautibrot6 formula in the .frm file below is evidently of sufficient generality to generate all of the various nautibrot(x) images that were previously posted. So the first thing I want to do is get L'Escargot entered right. ------------------------------parfile----------------------------- L'Escargot { ; July 31, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.par formulaname=nautibrot6 function=conj passes=b center-mag=-0.83436/0.180208/0.611899 params=4/1/-1/0 float=y colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } -------------------------------endpar----------------------------- This next image REALLY blows my mind... It's astonishing to me that patterns so strongly associated with the Fibonacci sequence and the golden mean should become utterly predominant, evidently, in a milieu where Feigenbaum's constant usually reigns. Has the former ratio actually entirely supplanted the latter, or do they exert a sort of shared influence, with the fractal perhaps somehow splitting differences between the two? Whatever the case, I about lost track of my time spent cycling diverse color maps through this rather elegant object; the one chosen here is from a recent Lee Skinner par. ------------------------------parfile----------------------------- Cornucopia { ; July 31, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=nautibrot6 function=exp passes=t center-mag=-0.86844/0.124809/0.611899 params=3/-2/-1/0 float=y colors=000000zr1zz1zzC<2>zzz<2>nsjQdrLdtblU<3>Mb8<3>LQ8KM8KJ8<2>\ I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8xu7zz5zz4zz3<\ 4>zj4zg4zc4<3>zS5zP5zL6zI6zE6wE6tD6<6>vAIv9Kv9M<3>x7Sy7Uy6Wz6Yz5\ _<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq0`v0d<2>y0f\ z0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5Xc6\ Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqvotvsww<2>zzz<3>rw\ zovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<3>SCCXCAaB9<3>uA2zA0xA0<12>SA1QA\ 1NA1<3>D92<6>UXAW`BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5f\ c0ce7_jFRoNIzb0zj0 } -------------------------------endpar----------------------------- The 'Radiance' image shows that a surprising symmetry is present when a purely imaginary value is assigned to the parameter p1. ------------------------------parfile----------------------------- Radiance { ; July 31, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=nautibrot6 function=conj passes=b center-mag=-2.39562/0.928852/0.2594452 params=0/4/-1/0 float=y colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } -------------------------------endpar----------------------------- This next is a bit whimsical: Save the image as a gif, open it in a small window and drag it about the screen; with the right settings (e.g., 'Show window contents while dragging') and a decent graphics card, you should see some very cool moire effects. This works for most of the others as well. ------------------------------parfile----------------------------- L'tl_L'es { ; July 31, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.par formulaname=nautibrot6 function=conj passes=b center-mag=-0.83436/0.180208/0.611899 params=2/1/-1/0 float=y colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } -------------------------------endpar----------------------------- I could not for some reason get this next one to render exactly in the #6 formula, so nautibrot4 is included. (Truly the 'naughtybrots' is what they should be called, since they don't behave at all like proper fractals.) So, OK, go ahead, color-cycle the Hypnoid... I dare ya! (but don't press "Enter" if you do...) ------------------------------parfile----------------------------- Hypnoid { ; July 31, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.par formulaname=nautibrot4 passes=3 center-mag=+0.98456120553466000/+0.17373634109460730/163.4115 params=4/1 float=y maxiter=1000 inside=0 outside=fmod colors=000CTT<3>8QR7PQ6PP5OP4NO<2>3OO3OP4OP<133>MvpMvpMvq<2>MwqM\ wqNvp<99>cWc } -------------------------------endpar----------------------------- ------------------------------frmfile----------------------------- frm:Nautibrot6 {;by Russ Walsmith z = 0, c = pixel, k=1, j=p2: j=j*(p2) k=p1*fn1(k)*j z = z^k + c z < 1000 } frm:Nautibrot4 { z = 0, c = pixel, k=1, j=-1: j=j*(-1) k=p1*conj(k)*j z = z^k + c z < 1000 } -------------------------------endfrms----------------------------

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FOTD 31-07-03 (Harlequin [5])
by Jim Muth 31 Jul '03

31 Jul '03

FOTD -- July 31, 2003 (Rating 5) Fractal visionaries and enthusiasts: The brilliant colors in today's image, which was produced by adding Z to Z^4, remind me of a harlequin's costume. I therefore named the image "Harlequin". The parent fractal is a Mandeloid with a lot of extra activity around the East Valley area. Today's scene is located deep in this activity. The image consists of a mixture of inside and outside material. The outside parts have been rendered in the traditional equal- iteration method; the inside however has been decorated with the 'fmod' inside fill. Since I had only limited time to find and color the image, I could not rate it at anything above average, though I did manage to give it a rating of a perfectly average 5. The render time of 10 minutes can be bypassed by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday featured a 2-1/2 hour power failure in the afternoon that put me behind in the work and kept it from being a perfect day. A man down the next block who thought he was a professional tree-trimmer turned out to be a total amateur. The partly sunny skies and temperature of 79F 26C were very comfortable for the hottest time of year. The cats were happy enough, since with the power off they had lots of supervised time in the yard. Today is starting cloudy and cool, with rain threatening. It remains to be seen how the rest of the day will go, but the best way I know to have a perfect day would be to find a perfect fractal. Will tomorrow be the day? Most likely not, but check to see how close it comes. Until then, take care, and as far as I know, the reality of fractals has never been determined. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Harlequin { ; time=0:10:34.39--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.04541673116753506/+0.062824240203421\ 91/1.00776e+012/1/-97.498923096774547/0.0005200442\ 07848097129 params=1/1/1/4/0/0 float=y maxiter=1000 inside=fmod symmetry=none periodicity=10 colors=000RaXTaYVaZXa`Zaa`abbacdadfaehagjahlainajp\ akqalsgetlZvrSwwLxzFvyHuvJtsLsqNrnPpkRohTnfVmcXl`Z\ kZ`iWbhTdgQffOheLjcIlbFnaDp`Ar_7tZ5uY7tX8rW9pWAnVB\ lUCjUDhTEgSGeSHcRIaQJ_QKYPLWONUOOTQQSSSRTUQVVPXWOY\ XN_YMaZLb`KdbJfdIgfHihGkjFlkEnmDpoCqpBsrAut9vu8xw7\ zy6zz6zr8yj9xbBwWCvOEuGFt9GuAHuBIuCJvCJvDKvELwELwF\ MwGNxGNxHOxIPyIPyJQyKRzKRzLSzMTzMTzNUzOVzOVxPWvQXs\ QYqRZnSZlS_iT`gUaeUacVcaWe`XgZYiXYkWZmU_oS`qRasPau\ NbwMcyKdzJdzRqtTpuUovWnvXmwYmw_lx`kxbjycjzGbRGSSGT\ TGUUGWVGVWGXXGXYGYZHY_IZ`J_aK`bL`cM_dNYgNWjNUlORoO\ PqOMtPJwPHyPEzPCzRFzTHyVJwWMtYOr_QpaSnbVkdXifZgg`e\ icbke`mgZnjWplUrnStpQusNwuLywJzyHyxIxxIwxJvxJuxKtw\ KswLrwLqwMpwMpwMovNnvNmvOlvOkvPjuPiuQhuQguRfuRfuRb\ sVZqYVoaSmdRlfQkhPjjOhmMgoLfqKesJcvIbxHazG`zJbxMct\ OdpRflTghWhdYia`kYclUemQhoMjpImqEorBr_CtHDdHOQHZBH\ hsKNnJPjJRfJSbIUZIWVIXRHZ } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 30-07-03 (Deep-Sea Scene [7])
by Jim Muth 30 Jul '03

30 Jul '03

FOTD -- July 30, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today might be the first time I have ever used the 'epsiloncross' inside fill in a FOTD fractal. This fill colors the points according to how close they come to the X and Y axes in their orbits. For some reason, this inside fill spreads into the outside areas as the proximity is raised. It has done this in today's image, where it has produced the fish-bone effect that inspired the name. The parent fractal was produced by taking plain Z and adding 1/20 part of Z^10 to it, then adding C. This parent resembles a M-set rotated 200 degrees, with a convergence of 9 valleys where its single East Valley should be. Today's scene is located in the fourth valley counting clockwise. While studying the image in search of a name, I at first could think of nothing. Then something in the picture reminded me of an underwater scene, and the 'epsiloncross' features started to look like fish skeletons. I named the image "Deep-Sea Scene" though it more closely resembles things that might be seen in shallow water. The rating of 7 is perhaps a bit high, but this is one of the few times, if not the only time I have used the 'epsiloncross' inside fill in a FOTD image, and that fact alone makes the image unique, or at least nearly so. The render time of 3 minutes is un-irritatingly short -- a real bargain for the time spent. Downloading the completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is equally efficient, assuming that the internet is not having one of its occasional bad days. Tuesday featured perfect weather and perfect cats here at Fractal Central. The blue skies were decorated with only a few angel-hair cirrus and cottonpuff cumulus clouds. The winds were light from the north, and the temperature reached only 81F 27C, at a time of year when near 90F 32C is normal. The cats spent several hours in the yard, meditating on whatever topic cats meditate on. Today's weather should be perfect once again. I expect the cats will be perfect also. Expect no surprises (other than the fractal) when the next FOTD appears in 24 hours. Until then, take care, and seek tranquility. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Deep-Sea_Scene { ; time=0:03:09.11--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.14224236936/-0.01022168581/35770.29/\ 1/-22.5/-2.3535721982437e-011 params=1/1/0.05/10/0\ /0 float=y maxiter=500 inside=epsiloncross proximity=0.0225 logmap=39 periodicity=10 colors=000K03zSCzNLsHUpMakJfgGo`DsYAvW8wTByQSzNXzK\ QzHNsEQhBUV8_PMjS_yVZqUZiUZaTZYTZWSZYSYWRYSRYSQYRP\ YRPXQOXQOXPNXPNXOMXOMZPP`QSbRUdSXmTZhUajVclWfnXhpY\ krYmF`3EV3CP2BJ2FM3IP4MR5PU6SW7WZ8Za9bcAefBhhC_l8R\ o5Jr2Kn8KkDLgILdNL`SMYYMUbNRgNNzNKqMJoLJmKIkJIiIHg\ HHeGGcFGaEF_DFYCEWBEUADS9DQ9DOCGLFJJILHLOFORDRTBUW\ 9WY7OdEHjL9qS2wZ3n_4f`5Z`6Ra6Ja6M`6P`6R`6U_6W_6Z_6\ `_6cZ6eZ6hZ6jZ6mY6oY6rY6tYAsWErUHqTLpROpPSoOVnMZmK\ amJXqVSueOxpGp_HqcIrfJsiJtlKupLvsMwvc4hKc1La5M`8N_\ BOYEPXHQWKRVNSTRTSUURXVQ_WObXNeYMhYLk_Qk`Vka_kbdkd\ ikenkfskgxkeyidzgczebzdazb`z`_zZZzYYzWXzUWzSVzRUzP\ TzNSzMWzSZzXazaRzJGz1NzCUzM`zWgzenzotzyuzvuzsuzpvz\ mvzkvzhwzewzbwz`xzYxzVxzSxzQizWWz`IzeMzdPzcTzbWza_\ z`bz_czddzidzmezrezvjzonziszbwzXvzYuzYtzYszZszZrzZ\ qzZpz_oz_oz_nz`mz`lz`lz`mzYnzWnzTozRpzOpzMqzJrzHrz\ EszCtz9KzSIzNGzJEzF000Az7 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 29-07-03 (Totally Ravishing [6])
by Jim Muth 29 Jul '03

29 Jul '03

FOTD -- July 29, 2003 (Rating 6) Fractal visionaries and enthusiasts: I was told that today's image is totally ravishing, which according to my dictionary means that viewing it causes indescribable delight. Well, I'm not fully convinced that my delight in viewing the image is indescribable, but the image is at least far enough above average to earn it a 6, so that's how I rated it. The name "Totally Ravishing" is an intentional exaggeration. The image is an evaporated one, with the inside activity made visible by the bof61 inside fill. The parent fractal in its un-evaporated form appears as a multi-bayed Mandeloid, its filaments leading to terminating rings. Today's scene is located in a cut-off feature close to a zig-zagging filament that runs down the center of a prominent valley. Although the resulting image was called 'totally ravishing', to me it appears to lack something. The colors, though brilliant, are not pure. A certain muddiness spoils things. And the elements have too many disquieting sharp points. The rating of 6 appears justified. The 5-minute render time is brief enough, but those with more pressing things to finish may save a few minutes by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The rain held off until after 3pm Monday here at Fractal Central, giving the cat duo time enough in the yard to make them happy before things got wet. The temperature of 82F 28C was no problem. Today is starting cool and sunny -- just the conditions to keep the duo happy. And the work shelf is piled just high enough to keep me busy until 2pm or so -- the conditions that keep me happy. It actually looks like a good day might be coming. Another FOTD is also coming, and it will appear in 24 hours. Until then, take care, and be of good cheer. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Totally_Ravishing { ; time=0:05:29.44--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.26428153306016700/+1.055502538839018\ 00/254505.2/1/70/8.99066862625197416e-010 params=7/-1.3/0.7/-13/0/1e+100 float=y maxiter=500 inside=bof61 outside=tdis periodicity=10 colors=000o`b6um0zo0zqzzzzsuz`XzVbxPgmLk`GqPCuE6z2\ 2zA0zH0zP0zX0zd0zk0zs0zz0zgCzRbz8zz0zz0zm0oP0X00G0\ 08CE0iL0`T0T`0Je0Cm02u00z00q00gC6`PER`NHmXAxd0zm0z\ u6zvHzvVzvezxszxzzxovz`mzNdz8Tz0Jz0A_08z06g06e04V2\ 4L8EHENGJXEPdCVmA`v8ez6VxNJsdAmu0gz0dz0so0zC0z00x0\ 0k40JH00X00i00e4Ed8VbGXVLXNTZGZZAb`8e`6gb6kb4od2qd\ 2ue0ve0zd0z`0zZ0zX0z`0zd0zg0zk0vGGV8bXAbXCdZEdZEe`\ GebHgbJgdLgdLieNigPkgRkiRmiTmkVokXomZooZqo`qqbsqds\ qdssduueuuguvivvkvxkxxmxzozzqzzqzzszzuzzvzzxzzxzzz\ zzzzzzzz82zC6zEAzHCzJGzNJzPLzRPzVTzXVz`Zzb`zddzggz\ iizmmzoqzqszuvzvzzzzzzzzZ0z`2z`4zb6zb8zdAzdCzdEzeG\ zeGzgHzgJzgLziNziPzkRzkTzkTzmVzmXzoZzo`zobzqdzqezs\ gzsgzsizukzumzvozvqzvszxuzxuzzvzzxzzzzzzzzzzzzzzzG\ 0zH2zJ4zL6zN8zPAzRCzTEzVGzVHzXJzZLz`NzbPzdRzeTzgVz\ iXziZzk`zmbzodzqezsgzuizvkzxmzxozzqzzszzuzzvzzxzzz\ zzzzG00L00R46VAE`HJdNRiTX } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 28-07-03 (The Quantum [7])
by Jim Muth 29 Jul '03

29 Jul '03

FOTD -- July 28, 2003 (Rating 7) Fractal visionaries and enthusiasts: For today's FOTD we return to a formula that has not been used for over a year. This formula, which draws nothing but empty circles, is named 'Mystic2'. I gave it this name because it is a near miracle that worthwhile fractals can come from it. But miracles sometimes do happen, and when we look at today's image, we are seeing a miracle in progress. The empty interiors produced by the Mystic2 formula are filled with unseen activity, which can be made visible by active inside fills such as the 'bof61' used in today's image. So today's image consists of nothing but inside material. There is nothing new in this -- the 'evaporated' images that I some- times post consist of all-inside material also. But at least, those 'evaporated' images were once real inside-outside images. Today's image never was real. It has no connection at all to fractal reality, whatever that is. Today's image, with its vaguely-defined, all-seeing eye, is all fuzziness, all uncertainty. It has no sharp edges. It reminds me of existence at the quantum level, where nothing is certain but uncertainty itself, and from some of the things I read, even the uncertainty is uncertain. I see probability clouds, where electrons might or might not exist at any point, and I see atoms, which are more real, but still far from the type of reality we think of when we observe the 'real' world around us. Thinking of how our oh-so-solid real world is built of less-than- solid blocks, I named today's image "The Quantum". I then rated it at an above-average 7. Of course, I am uncertain that this is the most correct rating. The 'Mystic2' formula creates far more than the simple fuzziness seen in today's image. It can create images indistinguishable from the normal equal-iteration-band pictures. It can create images like nothing seen before. I have no idea why I use it so rarely. Maybe I'll devote a month to 'Mystic2' images in the not-too-distant future. Today's image renders in 9 minutes, which is a bit slow. The download from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> will speed things quite a bit. Sunday was hot enough here at Fractal Central to satisfy the most ardent fan of high temperatures. The high temperature of 92F 33C set no record, but combined with the high humidity, it kept the dynamic fractal cats confined to the air conditioned indoors. They did venture outside briefly just before sunset, but the sound of a can of tuna being opened brought them scur- rying inside to eat. Today brings a threat of much rain and unhappy cats, so we'll have to see how it goes, and we'll need to have more tuna ready for distribution. Until next FOTD, which will appear as usual in 24 hours, take care, and live in your entire self. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Quantum { ; time=0:09:05.52--SF5 on a P200 reset=2002 type=formula formulafile=jim.frm formulaname=Mystic2 function=ident passes=1 center-mag=0.0540916/0.744129/30.70416 params=1.6/1.4/-0.1/-1.1/-1.6/-0.4 float=y maxiter=255 inside=bof61 logmap=yes periodicity=10 colors=000LH6LI6LI6LI6LJ6LJ6LK6MK5MK5RhzML5cVUdWUe\ XUfYUf_Vg`VhaVibVidVjeWkfWlgWliWmjWnkXolkonXptXqpX\ zsYrrXqqXqqWppWppVooVooUnnUnnTmmTmmSllSkkRkkRjjQjj\ QioPiiPwhPhhOggOggNffNeeMeeMddLddLccKccKbbJbbJaaIa\ aI``H__H__GZZGZZGYYFYYFXXEXXEWWDWWDVVCUUCUUBTTBTTA\ SSASS9RR9RR8QQ8PR7QQ8QQ8RQ9RQ9SQASPATPBTPBTPCUPCUO\ DVODVOEWOEWOFWOFXNGXNGYNHYNHZNIZMI_MJ_MJ_MK`MK`LLa\ LLaLMbLMbLNbLNcKOcKOdKPdKPeKQeJQfJRfJRfJSgJSgIThIT\ hIUiIUiIViIVjHWjHWkHXkHXlHYlGYmGZmGZmG_nG_nF`oF`oF\ apFapFbpFbqEcqEcrEdrEdsEesDetDftDftDguDguChvChvCiw\ CiwCjwCoxClwCjuChtCfrCdqCapC_nCYmCWkCUjCSiCPgCNfCL\ dCJcCHbCFcDHcDIcDKdDLdDNdDOdDPeDReDSeDUeDVfDWfDYfD\ ZgD`gDagDbgDdhDehDghDhpHtlFnhDidBd`9ZX8UT6PP4JL2EH\ 0AI19I19I29I29I29I39I39I49I49I49I59I59J68J68J68J78\ J78J88J88J88J98J98JA8JA8KA7KB7KB7KC7KC7KC7KD7KD7KE\ 7KE7KE7KF7LF6LG6LG6LG6LH6 } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Shear Amazement
by Russell Walsmith 28 Jul '03

28 Jul '03

Among other typos, L'escagot is supposed to be l'escargot... -- >L'escagot { ; July 23, '03 > ; Version 2002 Patchlevel 5 > reset=2002 type=formula formulafile=next.frm > formulaname=Nautibrot4 passes=3 > center-mag=-0.58651/0.281617/0.6666667 params=4/1 float=y > maxiter=300 > colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ > zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ > 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ > zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ > zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ > 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ > zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ > zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ > 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ > zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ > zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ > 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ > zk0kW0W > } > >------------------------------frmfile----------------------------- > >frm:Nautibrot4 { > z = 0, c = pixel, k=1, j=-1: > j=j*(-1) > k=p1*conj(k)*j > z = z^k + c > z < 1000 } > >-------------------------------endpar-----------------------------

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[Fractint] Re: I knew I had seen this before: Striking resemblance ; )
by JackOTradez 28 Jul '03

28 Jul '03

Yes! A hyper-velocity bullet on a mission of destruction. http://www.rumble.org/trans/trans6-21.jpg Ya gotta love it! Now we in my turf here. BTW, the extended (3 minute) version of the "Mosaic" viddie is unbelievable. Doesn't even look like fractals - loox like a 1970's time warp throwback. (Anyone remember Gold Windowpane or Blue Blotter ?) It is too big to post on the site - only for CD. Now lemme see what I can do with Russ' new formulas . . .. ... ..... ........ Stay Amazed. JoTz

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