📄 fractint.frm
字号:
z = Pixel:
z = ((z/2.7182818)^z)/sqr(6.2831853*z),
|z| <= 4
}
Sterling2(XAXIS) {; davisl
z = Pixel:
z = ((z/2.7182818)^z)/sqr(6.2831853*z) + pixel,
|z| <= 4
}
Sterling3(XAXIS) {; davisl
z = Pixel:
z = ((z/2.7182818)^z)/sqr(6.2831853*z) - pixel,
|z| <= 4
}
PsudoMandel(XAXIS) {; davisl - try center=0,0/magnification=28
z = Pixel:
z = ((z/2.7182818)^z)*sqr(6.2831853*z) + pixel,
|z| <= 4
}
{ These are the original "Richard" types sent by Jm Richard-Collard. Their
generalizations are tacked on to the end of the "Jm" list below, but
we felt we should keep these around for historical reasons.}
Richard1 (XYAXIS) {; Jm Richard-Collard
z = pixel:
sq=z*z, z=(sq*sin(sq)+sq)+pixel,
|z|<=50
}
Richard2 (XYAXIS) {; Jm Richard-Collard
z = pixel:
z=1/(sin(z*z+pixel*pixel)),
|z|<=50
}
Richard3 (XAXIS) {; Jm Richard-Collard
z = pixel:
sh=sinh(z), z=(1/(sh*sh))+pixel,
|z|<=50
}
Richard4 (XAXIS) {; Jm Richard-Collard
z = pixel:
z2=z*z, z=(1/(z2*cos(z2)+z2))+pixel,
|z|<=50
}
Richard5 (XAXIS) {; Jm Richard-Collard
z = pixel:
z=sin(z*sinh(z))+pixel,
|z|<=50
}
Richard6 (XYAXIS) {; Jm Richard-Collard
z = pixel:
z=sin(sinh(z))+pixel,
|z|<=50
}
Richard7 (XAXIS) {; Jm Richard-Collard
z=pixel:
z=log(z)*pixel,
|z|<=50
}
Richard8 (XYAXIS) {; Jm Richard-Collard
; This was used for the "Fractal Creations" cover
z=pixel,sinp = sin(pixel):
z=sin(z)+sinp,
|z|<=50
}
Richard9 (XAXIS) {; Jm Richard-Collard
z=pixel:
sqrz=z*z, z=sqrz + 1/sqrz + pixel,
|z|<=4
}
Richard10(XYAXIS) {; Jm Richard-Collard
z=pixel:
z=1/sin(1/(z*z)),
|z|<=50
}
Richard11(XYAXIS) {; Jm Richard-Collard
z=pixel:
z=1/sinh(1/(z*z)),
|z|<=50
}
{ These types are generalizations of types sent to us by the French
mathematician Jm Richard-Collard. If we hadn't generalized them
there would be --ahhh-- quite a few. With 11 possible values for
each fn variable,Jm_03, for example, has 14641 variations! }
Jm_01 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=(fn1(fn2(z^pixel)))*pixel,
|z|<=t
}
Jm_02 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=(z^pixel)*fn1(z^pixel),
|z|<=t
}
Jm_03 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1((fn2(z)*pixel)*fn3(fn4(z)*pixel))*pixel,
|z|<=t
}
Jm_03a {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1((fn2(z)*pixel)*fn3(fn4(z)*pixel))+pixel,
|z|<=t
}
Jm_04 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1((fn2(z)*pixel)*fn3(fn4(z)*pixel)),
|z|<=t
}
Jm_05 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2((z^pixel))),
|z|<=t
}
Jm_06 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2(fn3((z^z)*pixel))),
|z|<=t
}
Jm_07 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2(fn3((z^z)*pixel)))*pixel,
|z|<=t
}
Jm_08 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2(fn3((z^z)*pixel)))+pixel,
|z|<=t
}
Jm_09 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2(fn3(fn4(z))))+pixel,
|z|<=t
}
Jm_10 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2(fn3(fn4(z)*pixel))),
|z|<=t
}
Jm_11 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2(fn3(fn4(z)*pixel)))*pixel,
|z|<=t
}
Jm_11a {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2(fn3(fn4(z)*pixel)))+pixel,
|z|<=t
}
Jm_12 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2(fn3(z)*pixel)),
|z|<=t
}
Jm_13 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2(fn3(z)*pixel))*pixel,
|z|<=t
}
Jm_14 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2(fn3(z)*pixel))+pixel,
|z|<=t
}
Jm_15 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
f2=fn2(z),z=fn1(f2)*fn3(fn4(f2))*pixel,
|z|<=t
}
Jm_16 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
f2=fn2(z),z=fn1(f2)*fn3(fn4(f2))+pixel,
|z|<=t
}
Jm_17 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(z)*pixel*fn2(fn3(z)),
|z|<=t
}
Jm_18 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(z)*pixel*fn2(fn3(z)*pixel),
|z|<=t
}
Jm_19 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(z)*pixel*fn2(fn3(z)+pixel),
|z|<=t
}
Jm_20 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(z^pixel),
|z|<=t
}
Jm_21 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(z^pixel)*pixel,
|z|<=t
}
Jm_22 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
sq=fn1(z), z=(sq*fn2(sq)+sq)+pixel,
|z|<=t
}
Jm_23 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2(fn3(z)+pixel*pixel)),
|z|<=t
}
Jm_24 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z2=fn1(z), z=(fn2(z2*fn3(z2)+z2))+pixel,
|z|<=t
}
Jm_25 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(z*fn2(z)) + pixel,
|z|<=t
}
Jm_26 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
z=fn1(fn2(z)) + pixel,
|z|<=t
}
Jm_27 {; generalized Jm Richard-Collard type
z=pixel,t=p1+4:
sqrz=fn1(z), z=sqrz + 1/sqrz + pixel,
|z|<=t
}
Jm_ducks(XAXIS) {; Jm Richard-Collard
; Not so ugly at first glance and lot of corners to zoom in.
; try this: corners=-1.178372/-0.978384/-0.751678/-0.601683
z=pixel,tst=p1+4,t=1+pixel:
z=sqr(z)+t,
|z|<=tst
}
Gamma(XAXIS)={ ; first order gamma function from Prof. Jm
; "It's pretty long to generate even on a 486-33 comp but there's a lot
; of corners to zoom in and zoom and zoom...beautiful pictures :)"
z=pixel,twopi=6.283185307179586,r=10:
z=(twopi*z)^(0.5)*(z^z)*exp(-z)+pixel
|z|<=r
}
ZZ(XAXIS) { ; Prof Jm using Newton-Raphson method
; use floating point with this one
z=pixel,solution=1:
z1=z^z;
z2=(log(z)+1)*z1;
z=z-(z1-1)/z2 ,
0.001 <= |solution-z1|
}
ZZa(XAXIS) { ; Prof Jm using Newton-Raphson method
; use floating point with this one
z=pixel,solution=1:
z1=z^(z-1);
z2=(((z-1)/z)+log(z))*z1;
z=z-((z1-1)/z2) ,
.001 <= |solution-z1|
}
comment {
You should note that for the Transparent 3D fractals the x, y, z, and t
coordinates correspond to the 2D slices and not the final 3D True Color
image. To relate the 2D slices to the 3D image, swap the x- and z-axis,
i.e. a 90 degree rotation about the y-axis.
-Mark Peterson 6-2-91
}
MandelXAxis(XAXIS) { ; for Transparent3D
z = zt, ; Define Julia axes as depth/time and the
c = xy: ; Mandelbrot axes as width/height for each slice.
; This corresponds to Mandelbrot axes as
; height/depth and the Julia axes as width
; time for the 3D image.
z = Sqr(z) + c
LastSqr <= 4;
}
OldJulibrot(ORIGIN) { ; for Transparent3D
z = real(zt) + flip(imag(xy)), ; These settings coorespond to the
c = imag(zt) + flip(real(xy)): ; Julia axes as height/width and
; the Mandelbrot axes as time/depth
; for the 3D image.
z = Sqr(z) + c
LastSqr <= 4;
}
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