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4# 分形几何
这是源代码，代为上传：
global:
int n_attract = 4 ; number of attractors
int n_orbits ; number of orbits that have to be checked
if @giveup=="all done" || @giveup=="any done"
n_orbits = 2
else
n_orbits = 1
endif
; turning 'reorder' on will switch attractors 1 and 2 (of 0..3)
int ixA
int ixB
if @reorder
ixA = 1
ixB = 2
else
ixA = 2
ixB = 1
endif
init:
complex a = #pixel
complex attract[4] ; n_attract
complex orbit[2] ; n_orbits
attract[0] = -1
attract[ixA] = 1
; pre-calculate some factors outside the loop
complex tmps
complex fac0
complex fac2
if @pchoice=="halfdist"
attract[ixB] = @b-a
attract[3] = @b+a
fac0 = @b^2 - a^2
fac2 = fac0 - 1
tmps = @b^2 + 2*a^2 + 2
else ; @pchoice=="square"
complex tmp = sqrt(-a)
attract[ixB] = @b + tmp
attract[3] = @b - tmp
fac0 = @b^2 + a
fac2 = fac0 - 1
tmps = @b^2 - 2*a + 2
endif
if @giveup == "custom orbit start"
orbit[0] = @z_init
else
tmps = sqrt(tmps/3) / 2
$ifdef UNUSED
if real(tmps)*imag(@b) > -imag(tmps)*real(@b)
tmps = - tmps
endif
$endif
orbit[0] = @b/2 - tmps
orbit[1] = @b/2 + tmps
if @giveup == "other"
orbit[0] = orbit[1]
; orbit[1] = @b/2 - tmps ; not used in this case
endif
endif
z = orbit[0]-attract[0]
complex zprev = z ; give it some value to avoid compiler warnings
complex dist = 0 ; ditto
bool continue[2] ; n_orbits
continue[0] = true
continue[1] = true
int n_live ; how many orbits can bail out until we're done?
if @giveup=="all done"
n_live = n_orbits
else
n_live = 1
endif
int step=0 ; which attractor are we checking ? (with @stripes)
loop:
int ix = 0 ; count through the orbits
repeat
int found=-1
if continue[ix] ; orbit still live ?
z = orbit[ix]
if (@stripes)
; stripes: check only one attractor
dist = z-attract[step]
if |dist| < @delta
found=step
endif
else
; no stripes: check all attractors
int j=0 ; loop through the attractors
repeat
dist = z-attract[j]
if |dist| < @delta
found = j
endif
j=j+1
until j>=n_attract || found>=0
endif ; stripes
if (found>=0)
continue[ix] = false
n_live = n_live - 1
elseif (!@stripes || step==n_attract-1)
; here we step z (this is the core of the formula)
zprev = z
z = (3*z^4 - 4*@b*z^3 + fac2*z^2 + fac0) / ( 4*z^3 - 6*@b*z^2 + 2*fac2*z + 2*@b)
orbit[ix] = z
endif ; found
endif ; continue
ix = ix + 1
until ix >= n_orbits || n_live <= 0
if @stripes
step = step+1
if step >= n_attract
step = 0
endif
endif
; if we're bailing out, and zmode is != z, adjust the final z (for coloring algorithm)
if @zmode != "z"
if n_live <= 0
if @zmode=="distance"
z = dist
elseif @zmode=="step"
z = z-zprev
endif ; zmode
endif ; found
endif ; zmode
bailout:
; -- this isn't the bailout but the continuing condition
; false = bail; true = continue
n_live > 0
default:
title = "Newton-Mandel(a), degree-4 polynomial" ; v1.0
periodicity = 0 ; turn off periodicity checking by default as it interferes with 'stripes'
heading
caption = "Fractal shape"
endheading
param pchoice
caption="param interpretation"
enum="halfdist" "square"
default=0
endparam
complex param b
caption="b"
default=0
endparam
heading
caption = "Bailout"
endheading
float param delta
caption="Bailout delta"
hint="How close can z get to a fixed point? \
Actually, this is the square of the distance. \
Smaller values mean more iterations."
default=1e-10
min=0
endparam
param giveup
caption = "Stop when"
enum = "all done" "any done" "one" "other" "custom orbit start"
default = 0
endparam
complex param z_init
caption = "orbit start"
enabled = @giveup == "custom orbit start"
default = 0
endparam
heading
caption = "Coloring"
endheading
bool param stripes
caption="Staggered iteration"
hint="Checking this box means you can use one of the striped coloring methods. Use 4 stripes."
default=false
endparam
bool param reorder
; enabled = @stripes
default = false
caption = "Reorder attractors"
hint = "Exchange the attractors 1 and 2 (of 0..3). \
Matters if you use staggered iteration, or in the rare case when two attractors coincide."
endparam
param zmode
caption = "final z"
enum = "z" "distance" "step"
default = 1 ; "distance"
endparam
switch:
type = "N_Poly4_J"
pchoice = pchoice
a = #pixel
b = b
delta = delta
reorder = reorder
stripes = stripes
zmode = zmode
} |
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