################################################################# JoTz, What I understand of Periodicity Logic is that it is a speedup whose purpose is to decrease the calculation time of fractals by terminating a pixel's calculation early when Fractint detects that the values of the iterates have fallen into a repeating loop. This feature, which is on by default, operates on essentially all fractal calculations (probably not while calculating Iterated Function Systems) and can occasionally cause image artifacts most usually in the form of horizontal lines if the assumptions made for its correct operation are not met. Damien M. Jones notes that sometimes "'Holes' in an image while it is being drawn" can be an artifact caused by periodicity checking terminating an iteration too soon in certain circumstances. (See below.) Fortunately these problems seem not to happen too often -- since Mark Peterson's Periodicity Logic in Fractint has saved countless years while calculating fractals... :)

"...I think the effect looks rather cool..." The horizontal lines are really not supposed to be there. The lines are caused by the speedup algorithm going awry. However, one person's artifact can be another's nifty effect. I certainly have created some nice looking fractals with artifacts in them when writing my own code...

If I am correct, you can only turn this off with the command line parameter PERIODICITY=no (described below). There is no parameter on the V, X, Y or Z pages to turn this off. [Aside: A quick way to add a command line parameter to a calculation is with Robin Bussell's tiny (15kB) Windows 'front end' to DOS Fractint, called Paste 'n' Go. http://web.ukonline.co.uk/robin.b2/pastengo.htm You can specify any command line parameter in his Setup page as a 'Custom parm'. And of course you can paste (or type in) Fractint parameters and formulas into the text windows. Clicking 'Launch' copies the parameters and formulas to files which it 'feeds' to Fractint in an appropriate way. I use this program (under Win98) often and really like it a lot. Further Aside: I keep viewwindows=4/0.75/yes/0/0 as one of my custom parameters and always have it enabled so any fractal I start calculating appears in a 1/4 screen size viewing window to let me quickly see if things are going well. Then a quick 'v', 'n', 'Enter' starts drawing the fractal at full screen size. I am able to type all three characters without waiting for the text mode View Window Options screen to appear. Thanks again for a great program, Robin!] Note that PERIODICITY=no and PERIODICITY=0 do not do the same thing. Also, note that Ken Shirriff's inside coloring option 'Periodicity' (on the 'X' page and as a command line parameter - see below) determines pixel coloring. This setting/parameter does NOT turn on or off periodicity checking during the calculation of the fractal: "Inside=period colors pixels according to the period of their eventual orbit..." Btw, JoTz, Lee's recommendation of turning periodicity checking off while calculating your 'zoom2' fractal removed the horizontal lines from the image. JoTz's web site is at: http://www.sonic.net/~jot/ Click "The Ul†ima†e Frac†al Video Projec†!" link at the bottom of the page to see the animations he mentions in the message I quote at the bottom of this email. I am able to see this artifact in both 'Eye Of Hell #2' (very clearly) and 'Triskaidekaphobia'. Although I have not used them, JoTz appears to have written some very nice utilities for use with Fractint. JoTz, If you recalculate an image from one of your zooms would you please let me know whether turning periodicity checking off removes the horizontal lines from the image? Thanks... <--<< Also, what software do you use to combine Fractint's .gifs into an .wmv or .avi animation? <--<< Btw, your http://www.sonic.net/~jot/ufvp.html page is wider than my IE 6.0 browser set to full screen in 1024 x 768 screen size using 'Medium' (default) size characters. It only appears to exceed the screen width where Pen†aGo†h, KaLieÐesÇope and PyraMid appear side by side in a horizontal row not too far from the top of the page. Nice web site! Here is some info from the Fractint 20.0 docs about periodicity: - Hal Lane ######################### # hallane@earthlink.net # ######################### ====================== Fractint 20.0 Docs =========================== 8.2.1 Periodicity Logic The "Mandelbrot Lake" in the center of the M-set images is the traditional bane of plotting programs. It sucks up the most computer time because it always reaches the iteration limit -- and yet the most interesting areas are invariably right at the edge the lake. [Note: 'Lake' ares in other fractals have this same problem - Hal] (See The Mandelbrot Set (p. 35) for a description of the iteration process.) Thanks to Mark Peterson for pointing out (well, he more like beat us over the head until we paid attention) that the iteration values in the middle of Mandelbrot Lake tend to decay to periodic loops (i.e., Z(n+m) == Z(n), a fact that is pointed out on pages 58-61 of "The Beauty of Fractals"). An intelligent program (like the one he wrote) would check for this periodicity once in a while, recognize that iterations caught in a loop are going to max out, and bail out early. For speed purposes, the current version of the program turns this checking algorithm on only if the last pixel generated was in the lake. (The checking itself takes a small amount of time, and the pixels on the very edge of the lake tend to decay to periodic loops very slowly, so this compromise turned out to be the fastest generic answer). ... PERIODICITY=no|show|nnn Controls periodicity checking (see Periodicity Logic (p. 153)). "no" turns it off ... Type lambdafn function=exp needs periodicity turned off to be accurate -- there may be other cases. [And you seem to have found one in your 'zoom2' fractal and your Julia Set zooms -- Hal] ... Note that fractint normally uses periodicity checking to speed up bifurcation computation. However, in some cases a better quality image will be obtained if you turn off periodicity checking with "periodicity=no"; for instance, if you use a high number of iterations and a smooth colormap. ... "Holes" in an image while it is being drawn: Little squares colored in your "inside" color, in a pattern of every second square of that size, in solid guessing mode, both across and down (i.e., 1 out of 4), are a symptom of an image which should be calculated with more conservative periodicity checking than the default. See the Periodicity parameter under Image Calculation Parameters (p. 116). ... inside=atan colors by determining the angle in degrees the last iterated value has with respect to the real axis, and using the absolute value. This feature should be used with periodicity=0 ... Periodicity is a new inside coloring option. Thanks to Ken Shirriff. ... 5.9 Color Parameters INSIDE=nnn|bof60|bof61|zmag|attractor|epscross|startrail|period|fmod|atan Set the color of the interior ... Inside=period colors pixels according to the period of their eventual orbit. ... ====================== Fractint 20.0 Docs =========================== #################################################################

Date: Sun, 2 Nov 2003 10:24:01 -0500 From: "JackOTradez" <JackOTradez@email.msn.com> Subject: [Fractint] Re: Hal Lane;"zoom2"" To: <fractint@mailman.xmission.com> Message-ID: <000a01c3a155$5929ce70$06ec8041@skynet> Content-Type: text/plain; charset="iso-8859-1" Hal, I have seen this effect quite often over the past year; it is quite common in some Julia Set zooms, when you zoom into the black lake multicolored horizontal lines appear and finally the lake is filled with color. This can be seen in some of my animations, such as Eye Of Hell #2 and Triskaidekaphobia, and especially "Star Gate", which is no longer on my site (I can put it back up if anyone wants to see it). I also noticed it with some of the "multifractals" and other "unusual" fractals I have been playing with. Up till now I assumed it was a normal, if not understood, fractal phenomenon, and I have been pulling my hair out trying to figure it out. In animation sequences, it looks not unlike a "bifurcation" effect. Actually, I think the effect looks rather cool, especially with zoom animations. It never occured to me that it could be a "bug", or due to a fractint version, or a parameter tweak, as Lee suggested. I still don't know that it is. I will try Lee suggestions; I have not played much with periodicity setting, so I can tell you nothing about that. However, lowering the iteration count will often generate a fractal that looks completely different. BTW, I made an animation on a variation of the "Julia Rectangle" image, it is called Bad Trip and it is now on my site. Stay Amazed! JoTz #################################################################

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