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fractint-digest        Saturday, March 14 1998        Volume 01 : Number 133




----------------------------------------------------------------------

Date: Sat, 14 Mar 98 10:15:11 +0700
From: "Rob Fargher" <[e-mail]>
Subject: (fractint) Re: fractint-digest V1 #132

On Sat, 14 Mar 1998 05:48:18 -0700, Tim Wegner wrote:

>I should do this, I just need to get off my duff. Should it be
>fractint.org or fractint.com? What are the meanings of the domain
>names.

  Probably the .org domain would be more strictly correct but the
.com domain might be more useful.

  For instance, if you registered www.fractint.com, then anyone
using Netscape could just enter "fractint" in the Open dialog box and
Netscape would automatically resolve this to www.fractint.com.  I
don't think that a .org domain would be resolved.

  For most of us, whether it's .org or .com wouldn't matter but it
would be much easier for new folk to find a .com address.

Cheers,
Rob



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Date: Sat, 14 Mar 1998 09:55:47 -0700 (MST)
From: Kerry Mitchell <[e-mail]>
Subject: Re: (fractint) FRACTINT.ORG

Perhaps Tim et al would like to follow the model of POVRAY and go for
fractint.org.  Povray is a freeware ray-tracing program that was written
along the same lines as Fractint--massive contributions, a main core of
programmers, freely distributable, wonderful software.  Tim and other
Stone Soupers may have even been involved in povray's development.

Check it out at www.povray.org.  It has support for ray-tracing 4d
fractals (juliabrots, I think).

Kerry

- -------------------------------------------------------------------------------
Kerry Mitchell
[e-mail]
- -------------------------------------------------------------------------------


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Date: Sat, 14 Mar 1998 09:25:35 -0800
From: Mark Christenson <[e-mail]>
Subject: (fractint) A Fractal Voyage

For those who haven't seen my web site, I wanted to let you
know about a feature that will be going the way of the dinosaurs
shortly, due to an arbitrary server storage limit.  I have recently
touted Whole Earth Networks as an ISP worth checking into,
but their policies do have some downsides.  For $25/mo I get
full Internet service and 20 MB; to expand, I can pay an extra
$35/mo per 5MB or pay $100/mo for their "professional" account.
Not so hot, eh?  Actually, there is a less painful way, which
involves buying a second account and linking directories (so
$50/mo for 40MB).  In any case, I can't afford it.

The feature, "A Fractal Voyage", is no big deal.  It's just a deep
(although not by Fractint standards) Mandelbrot zoom,  but it has
a bit of a detective story behind it.  It will be there for two more
weeks.

Feature URL:
http://www.hooked.net/~mchris/room1d.htm

Fractint Gallery URL:
http://www.hooked.net/~mchris/fractint.htm

Home Page URL:
http://www.hooked.net/~mchris/fractals.htm


Bud


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Date: Sat, 14 Mar 1998 11:46:13 -0600
From: "Justin A. Kolodziej" <[e-mail]>
Subject: Re: (fractint) FRACTINT.ORG

Michael Traynor wrote:
>
> >> fractint.org or fractint.com?
>
> Both are kind of ironic, since the wonderful folk who have given us
> fractint are neither really an organization, nor are they a commercial
> endeavour.  Since one of the themes of fractals is apparent organization
> arising out of chaos, I'd go with .org (and send in $, but I'll have to
> run the gauntlet of the postal services, since money orders and checks for
> small amounts of foreign currency are expensive out of proportion and
> bothersome for the recipients, respectively - hope no dishonest posties
> are reading this!)
>

If you want something that's a little bit better, why not go for
www.fractint.ca?  After all, the main pages are on spanky.triumf.ca,
which sorta indicates that Canada is Fractint's home already.  Plus .ca
almost reminds me of ChAos! :-)

I just wonder what the restrictions are on using domain names reserved
for countries.  Does someone in that country have to register or what?

Just my $0.02 US (which is about the price domain names SHOULD be --
someone's getting awfully rich off of them!)

Justin K.
- --
I sense a great disturbance in the Source.
Justin A. Kolodziej
I am [e-mail]
Marquette University is http://www.mu.edu

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------------------------------

Date: Sat, 14 Mar 1998 12:14:02 -0600
From: "Tim Wegner" <[e-mail]>
Subject: Re: (fractint) FRACTINT.ORG

Kerry wrote,

> Check it out at www.povray.org.  It has support for ray-tracing 4d
> fractals (juliabrots, I think).

It sure does, but everything *except* julibrots. It does 4D
quaternion and hypercomplex fractals. I know because I programmed
this (in collaboration with others). I should try adding julibrots
too.

I'll respond to suggestions about domain names a bit later. I think
we should do it, but there are some issues to think through.

FWIW, you are right about www.povray.org, but we Lee Crocker uses
piclab.com.

Tim


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------------------------------

Date: Sat, 14 Mar 1998 10:18:40 -0800
From: Mark Christenson <[e-mail]>
Subject: Re: (fractint) FRACTINT.ORG

At 11:46 AM 3/14/98 -0600, Justin wrote:
>If you want something that's a little bit better, why not go for
>www.fractint.ca?  After all, the main pages are on spanky.triumf.ca,
>which sorta indicates that Canada is Fractint's home already.  Plus .ca
>almost reminds me of ChAos! :-)

I wouldn't object.  Canada is a nice, clean, modern, democratic place,
and its governments generally don't stick their collective nose into
other peoples' business or threaten to bomb them back to the stone
age (not that I think Saddam deserves any slack).  Hell, If I were two
years older (just turned 40), I might be living there instead of here
(USA; that pesky Vietnam thing, you know - 58,000 dead Americans,
and a lot more dead Vietnamese, for nothing).  The climate's a bit chilly,
though.

>Just my $0.02 US (which is about the price domain names SHOULD be --
>someone's getting awfully rich off of them!)

Word!  I just about passed a golden egg when I saw that $250 note.
That's why I don't have a domain name; I refuse to feed The Beast.
Wouldn't pay federal income tax, if I thought I could get away with it.


Bud


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------------------------------

Date: Sat, 14 Mar 1998 13:25:10 -0500 (EST)
From: [e-mail] (Kragen)
Subject: Re: (fractint) Color Maps

On Fri, 13 Mar 1998, Wizzle wrote:
> 7. Maps will be named to give credit to the author, i.e. wizzle1.map,
> gumbycat8.map, carlson3.map

Perhaps it would be better to let the authors decide what to name the
maps, allowing them to choose either self-promoting, creative, or
descriptive names -- or whatever else they choose.

Kragen


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------------------------------

Date: Sat, 14 Mar 1998 14:35:20 -0500 (EST)
From: [e-mail] (Kragen)
Subject: Re: (fractint) HARD HARDWARE QUESTION

On Sat, 14 Mar 1998, Paul Derbyshire wrote:
> Quake?
> 64 GIGS?!?!?!

64 gigs is reasonable these days.  I saw a supposedly-working 6.4G
drive sell on auctionweb yesterday for $225.  Probably you could put
together 64G of drive-space on a single machine for $3500 max, and
maybe much less.

(I'd be doing RAID4, though, with that much disk -- afraid of disk
failures if I had ten disks!)

I imagine the 64G is for fractals, though :)

Kragen


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------------------------------

Date: Sat, 14 Mar 1998 14:45:23 -0500 (EST)
From: [e-mail] (Kragen)
Subject: Re: (fractint) FRACTINT.ORG

On Sat, 14 Mar 1998, James R. McKenzie wrote:
> $100 for 2 years then $50 per anum heck yeah that\'s damn reasonable!

Actually, it costs the InterNIC approximately a dollar per domain per
year to maintain their database.  (And that's not counting the extra
services they provide, like randomly suspending your domain because they
forgot you paid, taking weeks to update your records, yanking your domain
because they decided that someone has a trademark on it, etc.)

I suggest that Tim register `fractint' as a trademark (which, I think,
costs $250) to give us a little safety.

> Who do I send the money order to (I prefer M.O.\'s)

I suggest Tim, as he's the current head of the development group.

> When or how soon?

InterNIC is very quick about creating new domains, since that's what
they get paid for.  Usually your domain will be happy the day the check
arrives -- or, if you pay by credit card, within minutes or hours.

The potentially slower part is finding two people with 24-7 Internet
access who are willing to act as DNS servers.  Lots of companies will
do this for you if you pay them, though.

Ideally, it should be two *different* entities, so that if there's a
flood in California, your DNS server in New York is still alive.

Kragen


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------------------------------

Date: Sat, 14 Mar 98 19:48:59 GMT
From: "John W. Evans" <[e-mail]>
Subject: Re: (fractint) FRACTINT.ORG

on 14 Mar 98, [e-mail] wrote...

>Wizzle wrote:
>
>> Good idea...
>>
>> Where do i send my check?  To whom do i make it out?
>
>Ditto....
>       --Andrew
>
>--
>| Andrew Duhan    |     Cereal is     |
>| [e-mail]  |       g00d.       |
>| http://chimera.acs.ttu.edu/~aduhan/ |
>
>
>
>-
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>
>
Ditto

John W. Evans


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------------------------------

Date: Sat, 14 Mar 1998 15:01:21 -0500 (EST)
From: [e-mail] (Kragen)
Subject: Re: (fractint) FRACTINT.ORG

On Sat, 14 Mar 1998, Justin A. Kolodziej wrote:
> If you want something that's a little bit better, why not go for
> www.fractint.ca?  After all, the main pages are on spanky.triumf.ca,
> which sorta indicates that Canada is Fractint's home already.  Plus .ca
> almost reminds me of ChAos! :-)
>
> I just wonder what the restrictions are on using domain names reserved
> for countries.  Does someone in that country have to register or what?

It varies from country to country.  For example, Tonga
(http://www.tonic.to/) registers domain names (at the same rate as the
InterNIC) for anyone in the world.

Canada (http://www.cdnnet.ca/) charges no fees (yet) for domain-name
registration.  There's a note on the introduction page:

Please note that the CA domain is for Canadian organizations.

The .ca registration process apparently takes a minimum of a week, and
apparently essentially requires that you either own a trademark or be
incorporated, in Canada.

> Just my $0.02 US (which is about the price domain names SHOULD be --
> someone's getting awfully rich off of them!)

According to
<URL:http://www.sec.gov/Archives/edgar/data/1030341/0000950133-97-003997.txt>,
Network Solutions' net income for the third quarter of 1997 was
$12,172,000.  (During the rest of 1997, it was $30,896,000, for a total
of $43,068,000.)

Kragen


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------------------------------

Date: Sat, 14 Mar 1998 14:09:32 -0600 (CST)
From: [e-mail] (Paul and/or Joyce Carlson)
Subject: Re: (fractint) Time for a newsgroup?

>I observe a steady stream of great new formulae coming from Paul
>Carlson and perhaps two or three others.  I doubt this is random
>formulizationizating.

I've been called a lot of things, but never a dirty, lowdown
random formulizationizater. :)

Seriously, my formulas usually do have some kind of logic to
them.  I've pretty much stopped putting a lot of comments in
my formulas because I sensed that not many people were interested
in how the formulas worked and those that were probably didn't
need the comments.

On the other hand, I have been thinking about posting a rather
detailed explanation about how I use orbit traps to give my
images a pseudo-3D look.  I would try to keep the math as
simple as possible.  Is there any interest in this?

>I suspect strongly that he knows what he is doing.

Aha! One more person I've fooled!

Paul Carlson



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------------------------------

Date: Sat, 14 Mar 1998 15:19:19 -0500
From: Gedeon Peteri <[e-mail]>
Subject: Re: (fractint) Time for a newsgroup?

Paul and/or Joyce Carlson wrote:

>  I have been thinking about posting a rather
> detailed explanation about how I use orbit traps to give my
> images a pseudo-3D look.  I would try to keep the math as
> simple as possible.  Is there any interest in this?

Yes.
Gedeon


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------------------------------

Date: Sat, 14 Mar 1998 14:23:52 -0600
From: Bob Margolis <[e-mail]>
Subject: Re: (fractint) List of URL's

The Most Honorable and Esteemed Tim Wegner wrote:
>
> >  - Anyone up for registering fractint.org?
>
> I should do this, I just need to get off my duff. Should it be
> fractint.org or fractint.com? What are the meanings of the domain
> names.
>

I see that the domain .com has been explained in previous postings. The
domain .org is for non-profit-making organizations such as the American
Red Cross and your local bar association. You have been reporting
Fractint's non-profit status to the IRS, haven't you, Tim? 8-)

Over to you.

Bob

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------------------------------

Date: Sat, 14 Mar 1998 13:12:33 -0600
From: "Damien M. Jones" <[e-mail]>
Subject: Re: (fractint) FRACTINT.ORG

Paul,

 - Registering a domain name with Internic Software will cost US$250.

Congratulations, you just got bilked.  Internic Software has nothing to do
with the InterNIC.  Internic Software is www.internic.com; the InterNIC is
www.internic.net.  Internic Software even says so, right on their home page.

The Internic Software price is inflated.  Many ISPs will offer you the
"service" of handling the domain name registration for you, but charge an
extreme price.  Their price may also include their own cost for "setting
up" the virtual host on their end.  The raw cost for registering a domain
name is $100, which is good for two years; after that, it's $50 per year.
I know, because I recently registered my own domain fractalus.com (and
because the InterNIC's FAQ still says it's $100).

The biggest problem is not the $100, but coming up with two domain name
servers for the new domain.  Typically, you must coordinate this with your
ISP or whoever is going to host the domain, and this is a big chunk of what
you pay money for.  After all, they are providing space and an IP address
for the domain (on one of their own servers, which acts as a host for lots
of virtual domains).  It pays to shop around for this, as rates vary widely.

One alternative to consider is a service like NameSecure
(http://www.namesecure.com) which will provide the DNS hosting and redirect
all web visitors to your domain to any URL you specify.  This is cheap, but
unless you have a server with its own IP address, the URL will change once
visitors arrive at the new site.  Still, it does let you reserve and use
the domain.  NameSecure charges $50 for the first year, and $25 for
subsequent years.

If that's a little too much initial outlay to get a domain started
(remember you still need to pay the InterNIC fee) then you can work through
GeoCities, which has a special deal with NameSecure.  GeoCities will give
you 3M for free, but if you sign up for GeoPlus, which is $5/mo., you can
get 15M of space.  Once you're in GeoPlus, you can then use NameSecure for
$5/mo. (rather than a $50 up-front fee).  This works out to $10 more for
the first year, but it's a little easier to swallow.  GeoCities is not an
unreasonable way to start hosting a web site; I ran fractalus.com from
there until December.

Damien M. Jones   \\
[e-mail]  \\  http://www.icd.com/tsd/ (temporary sanity designs)
                    \\  http://www.fractalus.com/ (fractals are my hobby)

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Date: Sat, 14 Mar 1998 14:40:44 -0600
From: Bob Margolis <[e-mail]>
Subject: Re: (fractint) Color Maps

Kragen wrote:
>
> Perhaps it would be better to let the authors decide what to name the
> maps, allowing them to choose either self-promoting, creative, or
> descriptive names -- or whatever else they choose.
>

My two drachmas worth:

I believe that the filename for a color map should be descriptive of
what the map looks like. If I saw wizzle.map, for instance, how would I
be able to remember that if had the colors, for example, blue, silver
and gold? Naming it something such as bluslvgd.map would be more helpful
in color map selections. If two or more people send in color maps with
the same name, such as orngblue.map, then they could be renamed
orngblu1.map and orngblu2.map.

Bob Margolis

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Date: Sat, 14 Mar 1998 14:43:22 -0600
From: "Damien M. Jones" <[e-mail]>
Subject: Re: (fractint) FRACTINT.ORG

Kragen,

 - InterNIC is very quick about creating new domains, since that's what
 - they get paid for.  Usually your domain will be happy the day the check
 - arrives -- or, if you pay by credit card, within minutes or hours.

My experience was that when InterNIC got my registration, the domain was
turned on.  I was billed by Network Solutions a week or so later, and I had
something like 30 days to pay the bill.  But the domain was up and running
long before I had actually paid for it.

 - The potentially slower part is finding two people with 24-7 Internet
 - access who are willing to act as DNS servers.  Lots of companies will
 - do this for you if you pay them, though.

Right.  I'd do it, but the company I work for has decided they're going to
start charging for such services. :(  Doesn't affect me, but it means I
can't host other domains for free.

 - Ideally, it should be two *different* entities, so that if there's a
 - flood in California, your DNS server in New York is still alive.

Ideally, but in practical situations it's less of an issue.  If my primary
DNS is in California, and so is my server (common) then it doesn't matter
if I have a backup DNS in New York, because if there's a flood in
California my server's underwater anyway. :)

Damien M. Jones   \\
[e-mail]  \\  http://www.icd.com/tsd/ (temporary sanity designs)
                    \\  http://www.fractalus.com/ (fractals are my hobby)

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Date: Sat, 14 Mar 1998 14:52:43 -0600
From: Bob Margolis <[e-mail]>
Subject: Re: (fractint) Time for a newsgroup?

The talented Paul and/or the pretty Joyce Carlson wrote:
>
>
> On the other hand, I have been thinking about posting a rather
> detailed explanation about how I use orbit traps to give my
> images a pseudo-3D look.  I would try to keep the math as
> simple as possible.  Is there any interest in this?
>

Would this be Pseudo-3-D Rendering Methods for Fractals in the Complex
Plane that appeared in Computers & Graphics, Vol 20, No.5, in 1996? If
so, I'm sure many programmers would be interested in your paper. This
was truly a well-written and informative report on Paul C's methods of
obtaining his gorgeous 3D effects.

Bob Margolis

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Date: Sat, 14 Mar 1998 15:33:18 -0600
From: "Justin A. Kolodziej" <[e-mail]>
Subject: Re: (fractint) FRACTINT.ORG

Kragen wrote:

> Canada (http://www.cdnnet.ca/) charges no fees (yet) for domain-name
> registration.  There's a note on the introduction page:
>
> Please note that the CA domain is for Canadian organizations.
>
> The .ca registration process apparently takes a minimum of a week, and
> apparently essentially requires that you either own a trademark or be
> incorporated, in Canada.

OK, so someone from Canada registers Fractint as a trademark and then
applies for the domain name.  Although then it would cost as much to get
fractint.ca as it would to get fractint.org... :-(

Guess that won't work.  And www.fractint.to  doesn't make much sense
either.

Sounds like www.fractint.org is the choice then.
Justin K.
- --
I sense a great disturbance in the Source.
Justin A. Kolodziej
I am [e-mail]
Marquette University is http://www.mu.edu

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Date: Sat, 14 Mar 1998 15:51:52 -0600 (CST)
From: [e-mail] (Paul and/or Joyce Carlson)
Subject: Re: (fractint) Time for a newsgroup?

>Bob Margolis wrote:
>>
>>
>> On the other hand, I have been thinking about posting a rather
>> detailed explanation about how I use orbit traps to give my
>> images a pseudo-3D look.  I would try to keep the math as
>> simple as possible.  Is there any interest in this?
>>
>
>Would this be Pseudo-3-D Rendering Methods for Fractals in the Complex
>Plane that appeared in Computers & Graphics, Vol 20, No.5, in 1996? If
>so, I'm sure many programmers would be interested in your paper. This
>was truly a well-written and informative report on Paul C's methods of
>obtaining his gorgeous 3D effects.
>
>Bob Margolis

No, what I had in mind was something more basic and detailed than my
Computers & Graphics article, which was written assuming a certain
level of knowledge of complex variables.  Also, the article (which I
actually wrote in 1995 - it took a year for it to be reviewed and
published) did not include some ideas I've come up with since I
wrote the article.

Paul Carlson


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------------------------------

Date: Sat, 14 Mar 1998 16:33:52 -0600 (CST)
From: [e-mail] (Paul and/or Joyce Carlson)
Subject: (fractint) Random Formulizationizating

Okay, so I do engage in a little random formulizationizating
from time to time in private behind locked doors (if I keep it up,
will I go blind?).  In this formula the equations being iterated
I just pulled out of the air - they have no significance that
I know of.  However, the image that the par produces is perfect
for zooming in on - the little balls that occur at all levels
of magnification all contain little Mandys and more little
balls.  Also, try color cycling this image.

Paul Carlson

frm:Formulization { ; Copyright (c) Paul W. Carlson, 1998
    z = w = iter = range_num = bailout = 0
    c = pixel
    p = p1 + p1
    num_ranges = real(p2)
    colors_in_range = imag(p2)
    colors_in_range_1 = colors_in_range - 1
    :
    ; Some random formulizationizating
    k = w * w + c
    w = k +  1 / (k * k) + k * c
    ;
    m = |w|
    IF ((p < p1) && (m > p1))
    bailout = 1
    index = colors_in_range_1 * (p1 - p) / p1
    z = index + range_num * colors_in_range + 1
    ENDIF
    p = m
    range_num = range_num + 1
    IF (range_num == num_ranges)
    range_num = 0
    ENDIF
    iter = iter + 1
    z = z - iter
    bailout == 0 && m < 100
}

rfm01              { ; Copyright (c) Paul W. Carlson, 1998
  reset=1960 type=formula formulafile=rndform.frm
  formulaname=formulization passes=t
  center-mag=0.510383/0.684126/11.22486
  params=4/0/8/30 float=y maxiter=500 inside=253 outside=summ
  colors=000rk0<4>zz0<12>aG00C4<15>0zR<12>0C40CC<15>0zz<12>0\
  CC00O<14>FFwGGzFFw<11>00OSA`<14>eNxfOzeNw<10>K2OO08<15>z0f\
  <13>O08O00<15>z88<12>O00c40<14>xU0zW0yU0<11>c40aG0<9>ph000\
  0<13>000 cyclerange=1/240
  }


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Date: Sat, 14 Mar 1998 17:53:05 -0800
From: Peter Jakubowicz <[e-mail]>
Subject: Re: (fractint) Time for a newsgroup?

At 03:51 PM 3/14/98 -0600, you wrote:

> On the other hand, I have been thinking about posting a rather
> detailed explanation about how I use orbit traps to give my
> images a pseudo-3D look.  I would try to keep the math as
> simple as possible.  Is there any interest in this?

Very much here.


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Date: Sat, 14 Mar 1998 15:18:02 -0800
From: John Wilson <[e-mail]>
Subject: (fractint) Re: Thank you note

Another "thank you" for your exposition regarding the basics of Fractint.
Ray Montgomery isn't the only "lurker" waiting for those pearls of wisdom
from the cognoscenti!  I guess that the "help" file will tell me all this
useful stuff, but personally I havn't yet stopped floundering around long
enough to actually RTFM.
Thanks again!  Please don't stop, this is appreciated.

Cheers,

John.


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Date: Sat, 14 Mar 1998 16:25:55 -0800
From: Mark Christenson <[e-mail]>
Subject: (fractint) guide for gravijul hunters

comment { commentary and pars (c) Mark "Bud" Christenson 3/14/98

I finally decided to stop groping around (not that it hasn't been fun)
and give myself a guide to gravijul - you guessed it, "gravibrot"!
I haven't navigated very far yet, but I *have* managed to find the
Mandelbrot Set among the debris.  I was certain it would be there,
and figured it would have something to do with inverse functions.

Happy hunting, Bud
}

gb05               { ; found the Mandelbrot (c) Bud 3/13/98
  reset=1930 type=formula formulafile=budz.frm formulaname=gravibrot
  function=ident/exp/log passes=t
  center-mag=4.44089e-015/-3.10862e-015/0.5 params=1/0/0/0/4/0 float=y
  inside=111
  colors=000SS_<3>cTgfUjhUkjUl<2>tYo<12>zz0<5>ct0_s0Ys3<14>0mz<14>TDwVAvX9\
  r<11>p15r00v00z00<30>YVVXXXXWX<29>y2yz0zz1y<23>zlEznCznC<35>zn1zm0zm0zl0\
  zl0<43>zU0zzz
  }

frm:gravibrot{ ; generalized r^(-2) by Mark "Bud" Christenson 3/13/98
; derived from gravijul
; defaults: p1 = (1,0) p2 = (0,0) p3 = (4,0)
   z = p2
   c = pixel:

   w = fn1(z)
   z = fn3(p1/fn2(w*w)) + c
    |z| < p3
  }



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Date: Sat, 14 Mar 1998 17:28:19 -0800
From: "Jay Hill"<[e-mail]>
Subject: Re: (fractint) guide for gravijul hunters

Hi Bud,

You missed half the fun....

gb05-b             { ; found the Mandelbrot (c) Bud 3/13/98
                     ; extend the bailout to greater range!!
  reset=1960 type=formula formulafile=mar98.par formulaname=gravibrot
  function=ident/exp/log passes=t
  center-mag=0.276642/-7.10543e-015/0.151088 params=1/0/0/0/120/0
  float=y inside=111
  colors=000SS_<3>cTgfUjhUkjUl<2>tYo<12>zz0<5>ct0_s0Ys3<14>0mz<12>PIwRFwTD\
  wVAvX9rZ8n<8>m2Dn29p15r00v00z00<30>YVVXXXXWX<29>y2yz0zz1y<23>zlEznCznC<3\
  3>zn2zn1zn1zm0zm0<45>zU0zzz
  }

frm:gravibrot{ ; generalized r^(-2) by Mark "Bud" Christenson 3/13/98
; derived from gravijul
; defaults: p1 = (1,0) p2 = (0,0) p3 = (4,0)
   z = p2
   c = pixel:

   w = fn1(z)
   z = fn3(p1/fn2(w*w)) + c
    |z| < p3
  }



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Date: Sat, 14 Mar 1998 19:54:02 -0800
From: Ryan Jameson <[e-mail]>
Subject: Re: (fractint) HARD HARDWARE QUESTION

At 02:35 PM 3/14/98 -0500, you wrote:
>64 gigs is reasonable these days.  I saw a supposedly-working 6.4G
>drive sell on auctionweb yesterday for $225.  Probably you could put
>together 64G of drive-space on a single machine for $3500 max, and
>maybe much less.
>
>(I'd be doing RAID4, though, with that much disk -- afraid of disk
>failures if I had ten disks!)
>
>I imagine the 64G is for fractals, though :)
>
>Kragen

You're right, I'd kill to have 64 gigs. My 6.4 gig ran out in about 4
months. I guess I'm just severly talented at filling up drive space....

Ryan

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Date: Sat, 14 Mar 1998 23:56:03 -0500 (EST)
From: [e-mail] (Paul Derbyshire)
Subject: Re: (fractint) HARD HARDWARE QUESTION

>(I'd be doing RAID4, though, with that much disk -- afraid of disk
>failures if I had ten disks!)

RAID4? WTF is RAID4?



- --
    .*.  Friendship, companionship, love, and having fun are the reasons for
 -()  <  life. All else; sex, money, fame, etc.; are just to get/express these.
    `*'  Send any and all mail with attachments to the hotmail address please.
Paul Derbyshire [e-mail] [e-mail]

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Date: Sat, 14 Mar 1998 23:02:49 -0600 (CST)
From: [e-mail] (Paul and/or Joyce Carlson)
Subject: (fractint) Pseudo 3D and Orbit Traps

Several people have indicated an interest in how I use orbit traps
to get a pseudo-3D effect in my fractals.  The following is an
attempt to explain the methods using as little math as possible.

I guess a good place to start might be to explain how I happened
to develop the 3D Stalks rendering method about 3 or 4 years ago.
I had written a program that plotted fractals using Pickover's
epsilon cross method.  With this method, when the orbitting point
lands within a specified distance, "epsilon," of either the real
or imaginary axis, bailout occurs and the screen pixel is plotted
in a color depending on the number of iterations at bailout.  The
result is an image consisting of stalks, each stalk being a solid
color.  I noticed that if I made epsilon smaller the stalks became
thinner and if larger the stalks became fatter.  I then modified
the program so that if the orbit point fell within a distance
epsilon of an axis the pixel was plotted red, but if the point fell
within a distance of one-half epsilon the pixel was replotted green.
The result was red stalks overlaid with green stalks about half
the thickness of the red stalks they were laying on.

These experiments showed me two things:  1) each stalk represents
a single iteration count at bailout, and 2) it was possible to
vary the color of the stalk depending on where within epsilon
the orbit point fell.  My first 3D Stalks image used only shades
of yellow - from bright yellow if the point fell exactly on one of
the axes to dark yellow if the point fell a distance epsilon away
from an axis, with intermediate shades of yellow for points falling
between those two extremes.  I used 250 shades of yellow, the
brightest at colormap index 1 and the darkest at colormap index 250
and the rest varying linearly in between (I usaully save colormap
index 0 for black since this is the overscan or border color).  My
program computed how close the orbit point fell to an axis and if
it was within epsilon the distance was saved in a variable "dist."
Then the ratio dist/epsilon was computed (call it "ratio") and used
to compute an index into the colormap as follows:

    index = 1 + ratio * 249

This gives values of index from 1 to 250 since ratio varies from
zero to one.  The resulting image consisted of yellow stalks, each
stalk being dark yellow at the edges and bright yellow in the center,
giving the stalks a 3D appearance since, everything else being equal,
bright portions of an image appear closer to the observer than dark
portions.

The next step was to break the colormap into two color ranges, index
1 to 125 light yellow to dark yellow, index 126 to 250 light blue
to dark blue.  The yellow range was used if bailout occurred on an
even iteration, the blue range if on an odd iteration, ie,

   if even, index =   1 + ratio * 124
   if odd,  index = 126 + ratio * 124

or, in general:

index = 1 + range_num * colors_in_range + ratio * (colors_in_range-1)

where range_num varies from zero to the number of color ranges minus
one.

This illustrates the basic pseudo-3D orbit trap method:

If an orbit point falls within the trap, compute the ratio of the
distance from the orbit point to some point Q in the trap divided by
the maximum distance from point Q to the boundary of the the trap
(this guarantees that the ratio will be from zero to one, inclusive)
and use that ratio to index into a color range.

Orbit traps can have many forms.  The main requirement is that the
test for the orbit point falling in the trap can't take too long to
execute since the test must be done every iteration.  Simple closed
areas like circles and squares make good orbit traps since it is easy
to test if the orbit point falls within them and it is also easy to
compute the ratio using the center of the area as point Q.  Plane
curves expressed in parametric form also make good orbit traps
except in this case the trap is a narrow constant width band with the
curve at its center (ie, for a circle the band would be a ring).
A formula I posted some time ago using an astroid curve illustrated
this: the argument of the iterated variable (the counter-clockwise
angle from the positive real axis to the orbit point) is computed
and used to compute the coordinates of point Q on the plane curve.
If the orbit point is within the specified distance of point Q,
compute the ratio and color index as above.

Sometimes for special effects I'll use color ranges in which the
colors do not vary linearly.  Sometimes I'll have the darkest shade
at both ends of the range with the brightest shade in the center of
the range.  Sometimes I'll use the ratio squared which emphasizes
the colors towards the beginning of a range.  Because the ratio
is always from zero to one, it can be raised to any positive power
and still be from zero to one.

The same general method of using a ratio between zero and one to
index into a color range is not limited to orbit traps.  In my
Atan method, for example, I use a ratio of angles.

To use these methods with Fractint I had to find a way to get
Fractint to use the computed colormap index.  I do this in my
formulas by iterating some variable other than z and by keeping
my own iteration counter.  Then when the point falls in the
orbit trap I set z equal to the colormap index minus the number of
iterations.  This works when outside=summ is used which adds
the number of iterations to z.

That's all I can think of for now.  I'll be glad to answer any
questions.

Paul Carlson


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End of fractint-digest V1 #133
******************************