ftp.xmission.com/2014.06.ftp.xmission.com.tar/ftp.xmission.com/pub/lists/fractint/archive/v01.n571

Internet Message Format | 2001-06-09 | 40KB

From: [e-mail] (fractint-digest)
To: [e-mail]
Subject: fractint-digest V1 #571
Reply-To: fractint-digest
Sender: [e-mail]
Errors-To: [e-mail]
Precedence: bulk


fractint-digest         Saturday, June 9 2001         Volume 01 : Number 571




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

Date: Sat, 09 Jun 2001 00:27:37 -0400
From: harry <[e-mail]>
Subject: Re: (fractint) Hairy Newton

Hairy Newton ???

Brother of "Fig" by any chance ???

BTW you are coming through in two's tonight....  Perhaps your
posts are bifurcating ???

H^) Harry (not Newton)

Multiple Bogeys wrote:

> Yesterday evening I set out to find an interesting family of
> Newton-based Mandelbrot mappings. The result was the collection of
> formulae below. You'll note the lack of 3D disease -- false alarm. All
> my posts to another listserv had it, but I now think it must be that
> listserv rather than MSN Exploder. Or rather, some interaction between
> the two (since some posts from that listserv don't have it), like the
> weird "email laser" that happened with this listserv last week (lots
> of peoples' messages were being duplicated, but for some reason mine
> were showing up in sets of five or six!)...Anyone who's an expert on
> listservs care to speculate further on what might be going on? One
> thing is clear: recent mail software and listservs have unnecessary
> complexity, and while we like complexity in our fractals, we could do
> without chaos erupting in the mail system we depend on to communicate
> here... The hrynewt_j and hrynewt_m formulae iterate Newton's method
> for p(z) = (z^n - 1)(z^3 - az - 1). Both n and a are parameters, as is
> the tolerance, an inverse bailout radius about the roots of p. The
> Mandelbrot variant has a vary over the screen while initial z is zero;
> this is a critical point but not a root of p for n real and greater
> than 2. You can plug in other values of n -- arbitrary negative or
> even complex values -- but won't generally be able to find minibrots
> unless n has a positive real part greater than two. If n is not an
> integer, there will be branch cuts in both the Mandelbrot and the
> Julia variants. The hrynewtnnn_j and _m formulae are optimized
> versions with specific values for n, mostly small positive integers.
> They avoid a slow arbitrary exponentiation, and for the smaller values
> of n re-use powers that are used on both sides of the polynomial or
> its derivative. The hrynewt2_m formula also has the feature of using a
> critical point for initial z, instead of zero (which is *not* a
> critical point for n = 2). The result is a proper Mandelbrot view, but
> it has a branch cut due to a square root in the calculation of the
> critical point, which is a-dependent. The branch cut has been
> intentionally manipulated to put it in a fairly unobtrusive place, but
> can't be eliminated; the full Mandelbrot for this one lives on a
> two-layer Riemann sheet like that of the square root function. The
> hrynewtnnn_m formulae also use an (XAXIS) symmetry declaration. (The
> generic hrynewt_m can't use this without trashing the output for
> non-real values of n.) Observations:* Certain choices of n produce
> three-fold-symmetric Mandelbrot sets. Find out which!* Mangled and
> occasionally also intact Mandelbrots can be extracted when n is
> "strange" but has a real part greater than 2.* You get radial petals
> with n real, concentric patterns with n imaginary, and logarithmic
> spirals with complex n; the ratio of   real to imaginary parts
> determines whether the spiral is steep (n close to real) or shallow (n
> close to imaginary).* The Mandelbrots are always quadratic -- for real
> n > 2, the critical point at zero is nondegenerate, and the critical
> point   pair for hrynewt2_m is degenerate only at one specific value
> of a. The formula file begins with an extensive comment that details
> the mathematical constructions that informed their design. comment {
>   We want a Newton's method with a large number of basins, most of
> which are fixed and predictable.
>   This is accomplished by choosing a polynomial function to solve
> composed of two factors, one with many fixed roots,
>   the other with a few mobile ones:
>   p(z) = (z^n-1)(z^3-az-1).
>   The Newton iteration is:
>   z -> r(z)
>   where
>   r(z) = z - p(z)/p'(z)
>        = (zp'(z) - p(z))/p'(z)
>   We easily discover p'(z) to be
>   p'(z) = (z^n-1)(3z^2-a) + (nz^(n-1))(z^3-az-1)
>         = (3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a
>   so
>   (zp'(z) - p(z)) = (z^n-1)(3z^3-az)+(nz^n)(z^3-az-1) -
> (z^n-1)(z^3-az-1)
>                   = (z^n-1)(2z^3+1)+(nz^n)(z^3-az-1)
>                   = (2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1
>   and
>   r(z) = ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 -
> 1)/((3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a)
>   Using the quotient rule the numerator of r'(z) is
>   ((3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a)((n+2)(n+3)z^(n+2) -
> an(n+1)z^n - n(n-1)z^(n-1) - 6z^2) -
>     ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)((n+2)(n+3)z^(n+1)
> - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
>   which factors into
>   ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
>   and
>   ((3+n)z^(n+3) - a(n+1)z^(n+1) - nz^n - 3z^3 + az) - ((2+n)z^(n+3) -
> anz^(n+1) - (n-1)z^n - 2z^3 - 1)
>   which simplifies to
>   z^(n+3) - az^(n+1) - z^n - z^3 + az + 1
>   Note that p(z) = z^(n+3) - az^(n+1) - z^n - z^3 + az + 1.
>   Thus the critical points of r(z) are the roots of p(z) and the roots
> of
>   q(z) := ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
>   These latter are the "interesting" critical points, as the other
> critical points of r(z) are all superattracting.
>   Note that q(z) is divisible by z, so 0 is an "interesting" critical
> point of r(z), for n not one of 2, 1, or -1.
>   This is the critical point used in the below hrynewt_m formulas
> except for hrynewt2_m. For n = 2,
>   q(z)/2 = 10z^3 - 3(a+1)z - 1
>   Put z = y + (a+1)/10y to get
>   q(z)/2 = y^6 - y^3/10 + (a+1)^3/1000
>   so
>   2y^3 = 1/10 +/-sqrt(1/100 - 4(a+1)^3/1000),
>   y = ((1/10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3)
>   and
>   z = ((1/10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3) + (a+1)/((1/10
> +/-sqrt(1/100 - 4(a+1)^3)/1000)/2)^(1/3)
> } hrynewt_j { ; p1 is Julia parameter, p2 is exponent n, p3 is
> tolerance (if 0, will act like 0.001).
>             ; SLOW. Use predefined hrynewtnnn_j where possible.
>   z = pixel, a = p1, n = p2, n1 = n - 1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = z^n1
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + n*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt_m { ; p2 is exponent n, p3 is tolerance (if 0, will act like
> 0.001).
>             ; SLOW. Use predefined hrynewtnnn_m where possible.
>   z = 0, a = pixel, n = p2, n1 = n - 1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = z^n1
>   zn = z*zn1
>   zno = (zn - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + n*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt2_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> act like 0.001).
>              ; n = 2.
>   z = pixel, a = p1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zno = (z2 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 2*z*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt2_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
>              ; n = 2.
>   a = pixel,
>   ap1 = a + 1,
>   IF((real(ap1) >= 0) || ((abs(real(ap1))*(3^(0.5))) <
> abs(imag(ap1))))
>     t = ((0.1 + (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),
>   ELSE
>     t = ((0.1 - (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),
>   ENDIF
>   z = t + 0.1*ap1/t, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zno = (z2 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 2*z*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt3_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> act like 0.001).
>              ; n = 3.
>   z = pixel, a = p1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zno = (z3 - 1)
>   zzz = zno - a*z
>   tz2 = 3*z2
>   pz = zno*zzz
>   ppz = zno*(tz2 - a) + tz2*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt3_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
>              ; n = 3.
>   z = 0, a = pixel, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zno = (z3 - 1)
>   zzz = zno - a*z
>   tz2 = 3*z2
>   pz = zno*zzz
>   ppz = zno*(tz2 - a) + tz2*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt4_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> act like 0.001).
>              ; n = 4.
>   z = pixel, a = p1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zno = (z*z3 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 4*z3*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt4_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
>              ; n = 4.
>   z = 0, a = pixel, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zno = (z*z3 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 4*z3*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt5_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> act like 0.001).
>              ; n = 5.
>   z = pixel, a = p1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = sqr(z2)
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 5*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt5_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
>              ; n = 5.
>   z = 0, a = pixel, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = sqr(z2)
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 5*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt17_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> act like 0.001).
>               ; n = 17.
>   z = pixel, a = p1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = sqr(sqr(sqr(z2)))
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 17*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt17_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
>
>               ; n = 17.
>   z = 0, a = pixel, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = sqr(sqr(sqr(z2)))
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 17*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt33_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> act like 0.001).
>               ; n = 33.
>   z = pixel, a = p1, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = sqr(sqr(sqr(sqr(z2))))
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 33*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> } hrynewt33_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
>
>               ; n = 33.
>   z = 0, a = pixel, r = p3
>   IF(r == 0)
>     r = 0.001
>   ENDIF
>   :
>   z2 = sqr(z)
>   z3 = z*z2
>   zn1 = sqr(sqr(sqr(sqr(z2))))
>   zno = (z*zn1 - 1)
>   zzz = (z3 - a*z - 1)
>   pz = zno*zzz
>   ppz = zno*(3*z2 - a) + 33*zn1*zzz
>   z = z - pz/ppz,
>   |pz| > r
> }
>
> -----------------------------------------------------------------------
> Get Your Private, Free E-mail from MSN Hotmail at
> http://www.hotmail.com.


- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

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

Date: Sat, 09 Jun 2001 01:26:59 -0500
From: [e-mail]
Subject: Re: (fractint) Hairy Newton

I'm getting Multiple Bogeys in Multiples tonight , too.

D. Freed

harry wrote:

> Hairy Newton ???
>
> Brother of "Fig" by any chance ???
>
> BTW you are coming through in two's tonight....  Perhaps your
> posts are bifurcating ???
>
> H^) Harry (not Newton)
>
> Multiple Bogeys wrote:
>
> > Yesterday evening I set out to find an interesting family of
> > Newton-based Mandelbrot mappings. The result was the collection of
> > formulae below. You'll note the lack of 3D disease -- false alarm. All
> > my posts to another listserv had it, but I now think it must be that
> > listserv rather than MSN Exploder. Or rather, some interaction between
> > the two (since some posts from that listserv don't have it), like the
> > weird "email laser" that happened with this listserv last week (lots
> > of peoples' messages were being duplicated, but for some reason mine
> > were showing up in sets of five or six!)...Anyone who's an expert on
> > listservs care to speculate further on what might be going on? One
> > thing is clear: recent mail software and listservs have unnecessary
> > complexity, and while we like complexity in our fractals, we could do
> > without chaos erupting in the mail system we depend on to communicate
> > here... The hrynewt_j and hrynewt_m formulae iterate Newton's method
> > for p(z) = (z^n - 1)(z^3 - az - 1). Both n and a are parameters, as is
> > the tolerance, an inverse bailout radius about the roots of p. The
> > Mandelbrot variant has a vary over the screen while initial z is zero;
> > this is a critical point but not a root of p for n real and greater
> > than 2. You can plug in other values of n -- arbitrary negative or
> > even complex values -- but won't generally be able to find minibrots
> > unless n has a positive real part greater than two. If n is not an
> > integer, there will be branch cuts in both the Mandelbrot and the
> > Julia variants. The hrynewtnnn_j and _m formulae are optimized
> > versions with specific values for n, mostly small positive integers.
> > They avoid a slow arbitrary exponentiation, and for the smaller values
> > of n re-use powers that are used on both sides of the polynomial or
> > its derivative. The hrynewt2_m formula also has the feature of using a
> > critical point for initial z, instead of zero (which is *not* a
> > critical point for n = 2). The result is a proper Mandelbrot view, but
> > it has a branch cut due to a square root in the calculation of the
> > critical point, which is a-dependent. The branch cut has been
> > intentionally manipulated to put it in a fairly unobtrusive place, but
> > can't be eliminated; the full Mandelbrot for this one lives on a
> > two-layer Riemann sheet like that of the square root function. The
> > hrynewtnnn_m formulae also use an (XAXIS) symmetry declaration. (The
> > generic hrynewt_m can't use this without trashing the output for
> > non-real values of n.) Observations:* Certain choices of n produce
> > three-fold-symmetric Mandelbrot sets. Find out which!* Mangled and
> > occasionally also intact Mandelbrots can be extracted when n is
> > "strange" but has a real part greater than 2.* You get radial petals
> > with n real, concentric patterns with n imaginary, and logarithmic
> > spirals with complex n; the ratio of   real to imaginary parts
> > determines whether the spiral is steep (n close to real) or shallow (n
> > close to imaginary).* The Mandelbrots are always quadratic -- for real
> > n > 2, the critical point at zero is nondegenerate, and the critical
> > point   pair for hrynewt2_m is degenerate only at one specific value
> > of a. The formula file begins with an extensive comment that details
> > the mathematical constructions that informed their design. comment {
> >   We want a Newton's method with a large number of basins, most of
> > which are fixed and predictable.
> >   This is accomplished by choosing a polynomial function to solve
> > composed of two factors, one with many fixed roots,
> >   the other with a few mobile ones:
> >   p(z) = (z^n-1)(z^3-az-1).
> >   The Newton iteration is:
> >   z -> r(z)
> >   where
> >   r(z) = z - p(z)/p'(z)
> >        = (zp'(z) - p(z))/p'(z)
> >   We easily discover p'(z) to be
> >   p'(z) = (z^n-1)(3z^2-a) + (nz^(n-1))(z^3-az-1)
> >         = (3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a
> >   so
> >   (zp'(z) - p(z)) = (z^n-1)(3z^3-az)+(nz^n)(z^3-az-1) -
> > (z^n-1)(z^3-az-1)
> >                   = (z^n-1)(2z^3+1)+(nz^n)(z^3-az-1)
> >                   = (2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1
> >   and
> >   r(z) = ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 -
> > 1)/((3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a)
> >   Using the quotient rule the numerator of r'(z) is
> >   ((3+n)z^(n+2) - a(n+1)z^n - nz^(n-1) - 3z^2 + a)((n+2)(n+3)z^(n+2) -
> > an(n+1)z^n - n(n-1)z^(n-1) - 6z^2) -
> >     ((2+n)z^(n+3) - anz^(n+1) - (n-1)z^n - 2z^3 - 1)((n+2)(n+3)z^(n+1)
> > - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
> >   which factors into
> >   ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
> >   and
> >   ((3+n)z^(n+3) - a(n+1)z^(n+1) - nz^n - 3z^3 + az) - ((2+n)z^(n+3) -
> > anz^(n+1) - (n-1)z^n - 2z^3 - 1)
> >   which simplifies to
> >   z^(n+3) - az^(n+1) - z^n - z^3 + az + 1
> >   Note that p(z) = z^(n+3) - az^(n+1) - z^n - z^3 + az + 1.
> >   Thus the critical points of r(z) are the roots of p(z) and the roots
> > of
> >   q(z) := ((n+2)(n+3)z^(n+1) - an(n+1)z^(n-1) - n(n-1)z^(n-2) - 6z)
> >   These latter are the "interesting" critical points, as the other
> > critical points of r(z) are all superattracting.
> >   Note that q(z) is divisible by z, so 0 is an "interesting" critical
> > point of r(z), for n not one of 2, 1, or -1.
> >   This is the critical point used in the below hrynewt_m formulas
> > except for hrynewt2_m. For n = 2,
> >   q(z)/2 = 10z^3 - 3(a+1)z - 1
> >   Put z = y + (a+1)/10y to get
> >   q(z)/2 = y^6 - y^3/10 + (a+1)^3/1000
> >   so
> >   2y^3 = 1/10 +/-sqrt(1/100 - 4(a+1)^3/1000),
> >   y = ((1/10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3)
> >   and
> >   z = ((1/10 +/-sqrt(1/100 - 4(a+1)^3/1000))/2)^(1/3) + (a+1)/((1/10
> > +/-sqrt(1/100 - 4(a+1)^3)/1000)/2)^(1/3)
> > } hrynewt_j { ; p1 is Julia parameter, p2 is exponent n, p3 is
> > tolerance (if 0, will act like 0.001).
> >             ; SLOW. Use predefined hrynewtnnn_j where possible.
> >   z = pixel, a = p1, n = p2, n1 = n - 1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = z^n1
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + n*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt_m { ; p2 is exponent n, p3 is tolerance (if 0, will act like
> > 0.001).
> >             ; SLOW. Use predefined hrynewtnnn_m where possible.
> >   z = 0, a = pixel, n = p2, n1 = n - 1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = z^n1
> >   zn = z*zn1
> >   zno = (zn - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + n*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt2_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> > act like 0.001).
> >              ; n = 2.
> >   z = pixel, a = p1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zno = (z2 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 2*z*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt2_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
> >              ; n = 2.
> >   a = pixel,
> >   ap1 = a + 1,
> >   IF((real(ap1) >= 0) || ((abs(real(ap1))*(3^(0.5))) <
> > abs(imag(ap1))))
> >     t = ((0.1 + (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),
> >   ELSE
> >     t = ((0.1 - (0.01 - 0.004*sqr(ap1)*ap1)^(0.5))/2)^(1/3),
> >   ENDIF
> >   z = t + 0.1*ap1/t, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zno = (z2 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 2*z*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt3_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> > act like 0.001).
> >              ; n = 3.
> >   z = pixel, a = p1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zno = (z3 - 1)
> >   zzz = zno - a*z
> >   tz2 = 3*z2
> >   pz = zno*zzz
> >   ppz = zno*(tz2 - a) + tz2*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt3_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
> >              ; n = 3.
> >   z = 0, a = pixel, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zno = (z3 - 1)
> >   zzz = zno - a*z
> >   tz2 = 3*z2
> >   pz = zno*zzz
> >   ppz = zno*(tz2 - a) + tz2*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt4_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> > act like 0.001).
> >              ; n = 4.
> >   z = pixel, a = p1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zno = (z*z3 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 4*z3*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt4_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
> >              ; n = 4.
> >   z = 0, a = pixel, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zno = (z*z3 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 4*z3*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt5_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> > act like 0.001).
> >              ; n = 5.
> >   z = pixel, a = p1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = sqr(z2)
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 5*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt5_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
> >              ; n = 5.
> >   z = 0, a = pixel, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = sqr(z2)
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 5*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt17_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> > act like 0.001).
> >               ; n = 17.
> >   z = pixel, a = p1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = sqr(sqr(sqr(z2)))
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 17*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt17_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
> >
> >               ; n = 17.
> >   z = 0, a = pixel, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = sqr(sqr(sqr(z2)))
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 17*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt33_j { ; p1 is Julia parameter, p3 is tolerance (if 0, will
> > act like 0.001).
> >               ; n = 33.
> >   z = pixel, a = p1, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = sqr(sqr(sqr(sqr(z2))))
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 33*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > } hrynewt33_m (XAXIS) { ; p3 is tolerance (if 0, will act like 0.001).
> >
> >               ; n = 33.
> >   z = 0, a = pixel, r = p3
> >   IF(r == 0)
> >     r = 0.001
> >   ENDIF
> >   :
> >   z2 = sqr(z)
> >   z3 = z*z2
> >   zn1 = sqr(sqr(sqr(sqr(z2))))
> >   zno = (z*zn1 - 1)
> >   zzz = (z3 - a*z - 1)
> >   pz = zno*zzz
> >   ppz = zno*(3*z2 - a) + 33*zn1*zzz
> >   z = z - pz/ppz,
> >   |pz| > r
> > }
> >
> > -----------------------------------------------------------------------
> > Get Your Private, Free E-mail from MSN Hotmail at
> > http://www.hotmail.com.
>
> --------------------------------------------------------------
> Thanks for using Fractint, The Fractals and Fractint Discussion List
> Post Message:   [e-mail]
> Get Commands:   [e-mail] "help"
> Administrator:  [e-mail]
> Unsubscribe:    [e-mail] "unsubscribe fractint"


- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

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

Date: Sat, 9 Jun 2001 05:16:02 -0400
From: "Multiple Bogeys" <[e-mail]>
Subject: (fractint) Bug

- ------=_NextPart_001_0000_01C0F0A3.46F0DE20
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

Try this:

1. Display some fractal from a type that has parameters. Set passes=3Dt.
2. Ctrl-E -- evolver/explorer. Turn it on. Use F6 and set two parameters =
to x and y respectively, leave the rest normal.
    Accept the F6 screen and change "show parameter zoom box" to "yes".
3. Page-up to get zoom box, move it with a ctrl-arrow, enter.
4. Space, turn off evolver/explorer, enter.
5. Observe something the manufacturer definitely didn't intend.
6. Hit 'b' to save parameters.
7. Observe something else the manufacturer didn't intend.

Type: bug
Reported-against: 20.01.10
Severity: low
Workaround: yes


Incidentally, the latest developer patches act weird when AF7 is bound to=
 1024x768x256 disk-video. Hitting it produces an error message that seems=
 to say something about not enough memory (on a 64 meg box!) after which =
it works anyway(!) -- this never occurred with 20.0 or 19.x.<br clear=3Da=
ll><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http:=
//www.hotmail.com">http://www.hotmail.com</a>.<br></p>

- ------=_NextPart_001_0000_01C0F0A3.46F0DE20
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>Try this:</DIV=
> <DIV> </DIV> <DIV>1. Display some fractal from a type that has par=
ameters. Set passes=3Dt.</DIV> <DIV>2. Ctrl-E -- evolver/explorer. Turn i=
t on. Use F6 and set two parameters to x and y respectively, leave the re=
st normal.</DIV> <DIV>    Accept the F6 screen and change =
"show parameter zoom box" to "yes".</DIV> <DIV>3. Page-up to get zoom box=
, move it with a ctrl-arrow, enter.</DIV> <DIV>4. Space, turn off evolver=
/explorer, enter.</DIV> <DIV>5. Observe something the manufacturer defini=
tely didn't intend.</DIV> <DIV>6. Hit 'b' to save parameters.</DIV> <DIV>=
7. Observe something else the manufacturer didn't intend.</DIV> <DIV>&nbs=
p;</DIV> <DIV>Type: bug</DIV> <DIV>Reported-against: 20.01.10</DIV> <DIV>=
Severity: low</DIV> <DIV>Workaround: yes</DIV> <DIV> </DIV> <DIV>&nb=
sp;</DIV> <DIV>Incidentally, the latest developer patches act weird when =
AF7 is bound to 1024x768x256 disk-video. Hitting it produces an error mes=
sage that seems to say something about not enough memory (on a 64 meg box=
!) after which it works anyway(!) -- this never occurred with 20.0 or 19.=
x.<BR><BR></DIV></BODY></HTML><DIV><BR><br clear=3Dall><hr>Get Your Priva=
te, Free E-mail from MSN Hotmail at <a href=3D"http://www.hotmail.com">ht=
tp://www.hotmail.com</a>.<br></p></DIV>

- ------=_NextPart_001_0000_01C0F0A3.46F0DE20--

- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

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

Date: Sat, 9 Jun 2001 06:04:19 -0400
From: "Multiple Bogeys" <[e-mail]>
Subject: Re: (fractint) Bug

- ------=_NextPart_001_0000_01C0F0AA.05960C00
Content-Type: text/plain; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

> Try this:

> 1. Display some fractal from a type that has parameters. Set passes=3Dt=
.
> 2. Ctrl-E -- evolver/explorer. Turn it on. Use F6 and set two parameter=
s to x and y respectively, leave the rest normal.
>    Accept the F6 screen and change "show parameter zoom box" to "yes".
> 3. Page-up to get zoom box, move it with a ctrl-arrow, enter.
> 4. Space, turn off evolver/explorer, enter.
> 5. Observe something the manufacturer definitely didn't intend.
> 6. Hit 'b' to save parameters.
> 7. Observe something else the manufacturer didn't intend.

Argh. That should have been:

1. Display some fractal from a type that has parameters. Set passes=3Dt.
2. Ctrl-E -- evolver/explorer. Turn it on. Use F6 and set two parameters =
to x and y respectively, leave the rest normal.
   Accept the F6 screen and change "show parameter zoom box" to "yes".
3. Page-up to get zoom box, move it with a ctrl-arrow, enter.
4. Space, turn off evolver/explorer, enter.
5. Observe something the manufacturer definitely didn't intend.
6. Page up, page up, enter to zoom in slightly, and observe something els=
e the manufacturer didn't intend.
7. Hit 'b' to save parameters.
8. Observe yet another behavior the manufacturer didn't intend.<br clear=3D=
all><hr>Get Your Private, Free E-mail from MSN Hotmail at <a href=3D"http=
://www.hotmail.com">http://www.hotmail.com</a>.<br></p>

- ------=_NextPart_001_0000_01C0F0AA.05960C00
Content-Type: text/html; charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable

<HTML><BODY STYLE=3D"font:10pt verdana; border:none;"><DIV>> Try this:=
</DIV> <DIV> </DIV> <DIV>> 1. Display some fractal from a type th=
at has parameters. Set passes=3Dt.</DIV> <DIV>> 2. Ctrl-E -- evolver/e=
xplorer. Turn it on. Use F6 and set two parameters to x and y respectivel=
y, leave the rest normal.</DIV> <DIV>>    Accept the F6=
 screen and change "show parameter zoom box" to "yes".</DIV> <DIV>> 3.=
 Page-up to get zoom box, move it with a ctrl-arrow, enter.</DIV> <DIV>&g=
t; 4. Space, turn off evolver/explorer, enter.</DIV> <DIV>> 5. Observe=
 something the manufacturer definitely didn't intend.</DIV> <DIV>> 6. =
Hit 'b' to save parameters.</DIV> <DIV>> 7. Observe something else the=
 manufacturer didn't intend.</DIV> <DIV> </DIV> <DIV>Argh. That shou=
ld have been:</DIV> <DIV> </DIV> <DIV> <DIV>1. Display some fractal =
from a type that has parameters. Set passes=3Dt.</DIV> <DIV>2. Ctrl-E -- =
evolver/explorer. Turn it on. Use F6 and set two parameters to x and y re=
spectively, leave the rest normal.</DIV> <DIV>   Accept the F6 =
screen and change "show parameter zoom box" to "yes".</DIV> <DIV>3. Page-=
up to get zoom box, move it with a ctrl-arrow, enter.</DIV> <DIV>4. Space=
, turn off evolver/explorer, enter.</DIV> <DIV>5. Observe something the m=
anufacturer definitely didn't intend.</DIV> <DIV>6. Page up, page up, ent=
er to zoom in slightly, and observe something else the manufacturer didn'=
t intend.</DIV> <DIV>7. Hit 'b' to save parameters.</DIV> <DIV>8. Observe=
 yet another behavior the manufacturer didn't intend.</DIV></DI=
V></BODY></HTML><DIV><BR><br clear=3Dall><hr>Get Your Private, Free E-mai=
l from MSN Hotmail at <a href=3D"http://www.hotmail.com">http://www.hotma=
il.com</a>.<br></p></DIV>

- ------=_NextPart_001_0000_01C0F0AA.05960C00--

- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

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

Date: Sat, 9 Jun 2001 07:32:46 -0500
From: "Jonathan Osuch" <[e-mail]>
Subject: (fractint) Fractint version 20.1.11

Fractint version 20.1.11 is now available on the developer's web site:
www.fractint.org

What's new:
Fixed a bug that caused a panned image to miss part of a line when the
  image was panned while the first row was being generated.

  Adjusted the time for keyboard checks when the showdot feature is used.
Now
  the iterations stop much quicker when a key is pressed.

  Fixed a problem with the float-only version that appeared when an
incomplete
  image was saved and restarted in the standard version.

  Fixed a problem in Xfractint pointed out by Ken on the Fractint bug list.

Jonathan



- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

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

Date: Sat, 9 Jun 2001 10:27:52 EDT
From: [e-mail]
Subject: (fractint) C-FOTD  09-06-01  (Chrysanthemums [4])

Classic FOTD -- June 09, 2001 (Rating 4)

Fractal visionaries and enthusiasts:

The run of exceptional fractals had to eventually come to an end.

Due to another busy day, today's image is not only late, but it
rates only a slightly below average 4.  The scene is one of a
midget in the Z^1.741101127 Mandeloid, lying 11 rotations up (or
is it down?) the logarithmic spiral.  The exponent is not random
however.  I intentionally chose the 5th root of 16, just to see
what would happen.

What happened is today's area of interesting chaos, featuring a
large but harmless chrysanthemum, which is infested by a spiral
and surrounded by countless smaller mums.

I doubt that the image is worth the 25 minutes it takes to draw
it from the attached parameter file.  A trip to:

          <http://home.att.net/~Paul.N.Lee/FotD/FotD.html>

or to:

          <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>

to download the image is recommended

The fractal weather today was uneventful, with lots of sun and a
temperature of 81F (27C).  The cats enjoy uneventful weather, so
they were happy.

it's now already 10:20am of Saturday morning, and I've got
chores to do around Fractal Central.  Until next time, take
care, and what is the meaning of fractals?


Jim Muth
[e-mail]


START 20.0 PAR-FORMULA FILE================================

Chrysanthemums     { ; time=0:25:47.03--SF5 on a P200
  reset=2001 type=formula formulafile=allinone.frm
  formulaname=MandelbrotBC1 function=floor passes=1
  center-mag=-0.010176721962093/-0.348637919700844/2\
  682929/1/57.499 params=1.741101127/0/11/0 float=y
  maxiter=10000 inside=0 logmap=-686 periodicity=10
  colors=000FA0HD0IE0IF0JI0KJ0MK0MM0SK2ZJ2eI3kH3qF3n\
  J8kMDiOHfSKcVOaYUZaYXcaUfeRjiOmnMorJsvHvzEyzFvzFsz\
  HqyHnvHkuIjsIgqIeoJbnJ_kJZjKXiKUfMReMOcMMaNK_RIZNF\
  XO0POAUO8SZKUiXVsgXzrYzn_zkazibzfczcezafzZgzXizUjz\
  RkzOmzMnzGozYqzcrzmszmuzhvzcwzZyzUzzPvzKsyFoyAmwDi\
  wFfvIcvK_uNYuQUsSRsVOrYKr_IqbEqeBog8oj4nm2no0mr0mu\
  0nr0oo0om0qj3rg6re8sbBuaEuZHvXJwUMwROyORzMUzKXvMVr\
  NVoNVkOVgOVeQVaQVZRVVSVRSVOUVKUVHVVEVVAXV7XVBYSFZR\
  J_QNaORbNVbMZcKbeJffIjgHniFriEvjDzkBzmAzn8zn7oc3VV\
  0AK00B00I07O0FV0N_0Vf0bm3jr4ry7zz8zzAzz7zz4zz2zz0z\
  z0zz0zz0zy0zu0zr0yn0vk0ug0re0qa0nZ0mV0jS0iO0gM0ZaE\
  RqUJzgKzeMzcMzbNyaNw_OvZOuYQrXQqVRoURnSSmRSkQUjOUi\
  NSeJSaHSZESVARS7RO4RM0RI0RF0UI0XK4YMA_OEbRIcSNfVRi\
  YVjZ_macocgqemsgqvjuwkzznzzozzqzzrzzswzusyvoywmyyi\
  yzfwzbwzZwzXwzSvzOvzMvzIvzFwzIwzKwzNwzOwzRwzUwzVwz\
  Ywz_wzbwzcwzfyziyzjyzmyzo
  }

frm:MandelbrotBC1   { ; by several Fractint users
  e=p1, a=imag(p2)+100
  p=real(p2)+PI
  q=2*PI*fn1(p/(2*PI))
  r=real(p2)-q
  Z=C=Pixel:
    Z=log(Z)
    IF(imag(Z)>r)
      Z=Z+flip(2*PI)
    ENDIF
    Z=exp(e*(Z+flip(q)))+C
  |Z|<a
}

END 20.0 PAR-FORMULA FILE==================================

- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

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

Date: Sun, 10 Jun 2001 03:19:13 +0200
From: "Jean-Pierre SEIMAN" <[e-mail]>
Subject: (fractint) Fractint20 with Windows98

C'est un message de format MIME en plusieurs parties.

- ------=_NextPart_000_000B_01C0F15C.1F933440
Content-Type: text/plain;
    charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable

Question from a new user of Fractint 20 (DOS)

How may Y use it with Windows?

Which are the settings?

Thank you in advance?

Jean-Pierre

- ------=_NextPart_000_000B_01C0F15C.1F933440
Content-Type: text/html;
    charset="Windows-1252"
Content-Transfer-Encoding: quoted-printable

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Dwindows-1252">
<META content=3D"MSHTML 5.50.4611.1300" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<DIV><FONT face=3DTahoma color=3D#008000>Question from a new user of =
Fractint 20=20
(DOS)</FONT></DIV>
<DIV><FONT face=3DTahoma color=3D#008000></FONT> </DIV>
<DIV><FONT face=3DTahoma color=3D#008000>How may Y use it with =
Windows?</FONT></DIV>
<DIV><FONT face=3DTahoma color=3D#008000></FONT> </DIV>
<DIV><FONT face=3DTahoma color=3D#008000>Which are the =
settings?</FONT></DIV>
<DIV><FONT face=3DTahoma color=3D#008000></FONT> </DIV>
<DIV><FONT face=3DTahoma color=3D#008000>Thank you in =
advance?</FONT></DIV>
<DIV><FONT face=3DTahoma color=3D#008000></FONT> </DIV>
<DIV><FONT face=3DTahoma =
color=3D#008000>Jean-Pierre</FONT></DIV></BODY></HTML>

- ------=_NextPart_000_000B_01C0F15C.1F933440--


- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

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

Date: Sun, 10 Jun 2001 15:45:45 +1200
From: "Morgan L. Owens" <[e-mail]>
Subject: Re: (fractint) Fractint20 with Windows98

At 13:19 10/06/2001, you wrote:
>Question from a new user of Fractint 20 (DOS)
>
>How may Y use it with Windows?
>
>Which are the settings?
>
>Thank you in advance?
>
>Jean-Pierre

A page that covers this issue can be found at
http://spanky.triumf.ca/www/fractint/fracwin95.html.

Win98 isn't too different - it's just Win95 released three years after
deadline. Now, if you'd asked about Windows Millennium or Win2000 ...

You might want to run makefcfg.exe first, to get a customised video mode
config file.

Morgan L. Owens
"MS-DOS is a relicensing of something called 'Quick and Dirty Operating
System'. Says it all, really..."


- --------------------------------------------------------------
Thanks for using Fractint, The Fractals and Fractint Discussion List
Post Message:   [e-mail]
Get Commands:   [e-mail] "help"
Administrator:  [e-mail]
Unsubscribe:    [e-mail] "unsubscribe fractint"

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

End of fractint-digest V1 #571
******************************