xnew = xold, if xold <= 1, andWhen xnew is plotted vs. xold, a tent shape results, with the peak at the critical point, xold = 1.
xnew = 2 - xold, if xold > 1.
To use this formula with a complex variable z, a way is needed to generate a real value for the tent map. These formulas offer several: magnitude of z, real part, imaginary part, imaginary/real, and real*imaginary. Also, different rotational modes are offered. For example, instead of using just the real part of z, maybe the 45 degree line y = x is taken as the new "x" axis for the tent map. This rotation can be done is several ways.
general-tent-sample1 { ; copyright Kerry Mitchell 01oct2000
;
; Sample of the General Tent formula
; using 'imaginary part' r type and 'constant' rotation
; of 45 degrees
;
fractal:
title="General Tent Sample 1" width=480 height=480 author="Kerry
Mitchell"
created="October 1, 2000" numlayers=2
layer:
method=multipass caption="New Layer 2" opacity=100 visible=yes
alpha=no
mergemode=multiply
mapping:
center=0/0 magn=2.4 angle=340
formula:
filename="lkm.ufm" entry="general-tent-julia" maxiter=1000
percheck=off
p_julparam=1.0513704938994191/0.498206243061781633 p_bailout=1000000
p_rtype="imag part" p_rottype="constant" p_rotamount=45
p_rotunit="degrees"
inside:
transfer=none repeat=yes
outside:
filename="lkm.ucl" entry="rose-range-lite" density=3 transfer=linear
repeat=yes p_scale=0.75 p_rangewidth=0.5 p_colorby="last
angle" p_ac=1
p_bc=3 p_as=0 p_bs=0 p_curvecenter=0/0 p_rot=0
gradient:
smooth=yes numnodes=4 index=0 color=4308801 index=100 color=0
index=200
color=4308801 index=300 color=16777215
layer:
method=multipass caption="New Layer 1" visible=yes alpha=no
mapping:
center=0/0 magn=2.4 angle=340
formula:
filename="lkm.ufm" entry="general-tent-julia" maxiter=1000
percheck=off
p_julparam=1.0513704938994191/0.498206243061781633 p_bailout=1000000
p_rtype="imag part" p_rottype="constant" p_rotamount=45
p_rotunit="degrees"
inside:
transfer=none repeat=yes
outside:
filename="lkm.ucl" entry="rose-range-lite" transfer=linear
repeat=yes
p_scale=0.75 p_rangewidth=0.5 p_colorby="last magnitude"
p_ac=1 p_bc=3
p_as=0 p_bs=0 p_curvecenter=0/0 p_rot=0
gradient:
smooth=yes numnodes=4 index=0 color=0 index=100 color=4308801
index=200
color=16777215 index=300 color=4308801
}
general-tent-sample2 { ; copyright Kerry Mitchell 02oct2000
;
; Sample of General Tent formula
; using 'magnitude' r type and 'none' rotation
;
fractal:
title="General Tent Sample 2" width=480 height=480 author="Kerry
Mitchell"
created="October 2, 2000" numlayers=1
layer:
caption="Layer 1" visible=yes alpha=no
mapping:
center=1.23/1.55 magn=0.7 angle=0
formula:
filename="lkm.ufm" entry="general-tent-julia" maxiter=1000
percheck=off
p_julparam=-0.43033100872625215/0.937762375451733166 p_bailout=1000000
p_rtype="magnitude" p_rottype="none" p_rotamount=45 p_rotunit="degrees"
inside:
transfer=none repeat=yes
outside:
density=3 transfer=sqrt repeat=yes
gradient:
smooth=yes numnodes=4 index=84 color=0 index=183 color=4292799
index=283
color=16777215 index=383 color=4292799
}
general-tent-sample3 { ; copyright Kerry Mitchell 02oct2000
;
; Sample of General Tent formula
; using 'real part' r type and 'progressive' rotation type
; of 180 degrees
;
fractal:
title="General Tent Sample 3" width=600 height=200 author="Kerry
Mitchell"
created="October 2, 2000" numlayers=2
layer:
method=multipass caption="New Layer 2" opacity=100 visible=yes
alpha=no
mergemode=difference
mapping:
center=1/0 magn=1 angle=315
formula:
filename="lkm.ufm" entry="general-tent-julia" maxiter=1000
percheck=off
p_julparam=0/1.41421356237309505 p_bailout=1000000 p_rtype="real
part"
p_rottype="progressive" p_rotamount=180 p_rotunit="degrees"
inside:
transfer=none repeat=yes
outside:
filename="lkm.ucl" entry="conic-lite" transfer=sqrt repeat=yes
p_type="circle" p_center=0/0 p_theta=45 p_radius=1 p_xaxis=1.5
p_yaxis=0.75 p_colorby="minimum distance"
gradient:
smooth=yes numnodes=4 index=50 color=12542017 index=150
color=16777215
index=250 color=4300991 index=349 color=0
layer:
method=multipass caption="New Layer 1" visible=yes alpha=no
mapping:
center=1/0 magn=1 angle=315
formula:
filename="lkm.ufm" entry="general-tent-julia" maxiter=1000
percheck=off
p_julparam=0/1.41421356237309505 p_bailout=1000000 p_rtype="real
part"
p_rottype="progressive" p_rotamount=180 p_rotunit="degrees"
inside:
transfer=none repeat=yes
outside:
filename="lkm.ucl" entry="conic-lite" transfer=sqrt repeat=yes
p_type="line" p_center=1/0 p_theta=-45 p_radius=1 p_xaxis=1.5
p_yaxis=0.75 p_colorby="minimum distance"
gradient:
smooth=yes numnodes=2 index=50 color=16777215 index=250
color=0
}