[Fractint] Horizontal line (and other) artifacts due to periodicity testing

6 Nov 2003

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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 UlÂimaÂe FracÂal Video ProjecÂ!" 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 PenÂaGoÂh, KaLieÃesÃope 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

====================== Fractint 20.0 Docs ===========================

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...
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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