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Author Topic: best program that includes orbit display?!?!  (Read 1187 times)
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cKleinhuis
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« on: October 19, 2012, 12:46:23 AM »

hi there,

i wonder which program is able to visualise the orbit of a point in the complex plane ?! as far as i know ultrafractal can not do it ....
sad

would love to demonstrate the listeners of my seminar the process of orbits
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Sockratease
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« Reply #1 on: October 19, 2012, 12:52:41 AM »

Fractal Science Kit does this - but the trial watermarks everything, even just using it.

Maybe Ross would let you have a copy for your lectures?
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blob
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« Reply #2 on: October 19, 2012, 01:47:35 AM »

GruFi Fractal Generator http://sourceforge.net/projects/grufifractalgen/
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cKleinhuis
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« Reply #3 on: October 19, 2012, 02:48:27 AM »

thx blob and sock, will check out the generator, and if i am not convinced i am going to ask ross wink
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cKleinhuis
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« Reply #4 on: October 19, 2012, 02:54:17 AM »

i see, great, the grufi generator works just fine for demonstration of it behaves!
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David Makin
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« Reply #5 on: October 19, 2012, 04:24:08 AM »

hi there,

i wonder which program is able to visualise the orbit of a point in the complex plane ?! as far as i know ultrafractal can not do it ....
sad

would love to demonstrate the listeners of my seminar the process of orbits


Ultrafractal can do anything !!

mmf4.ufm-Attractors

Default is Mandelbrot mode - using the switch by default displays the orbits but you can change this between Julia and Orbits.
** Read the help text at the top of the paramaeters **


Edit: I forgot - after switching to the orbit view change the main UF max. iterations to 1 and set the inside colouring to black - also increase the max. hits ans orbit iterations in the formula - here's a good one to switch from to start with:

Code:
Fractal1 {
fractal:
  title="Fractal1" width=928 height=696 layers=1
  credits="Dave Makin;10/19/2012;D J Makin;12/20/2011;Dave Makin;10/5/\
  2011;David Makin;6/15/2008;Frederik Slijkerman;7/23/2002"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=0.456457839/0.00599907825 magn=1.5655146
formula:
  maxiter=2000 percheck=off filename="Mmf4.ufm"
  entry="MMF4a-AttractorsPlus" p_version=3 p_mandy=yes p_orbit=no
  p_showinfo=yes p_julia=no p_progress=None p_bailtest=Both
  p_smallbail=1E-9 p_bailout=65536.0 p_lyapunov=no p_lbail=0.05
  p_lbail1=1.0 p_fdim=no p_fbail=0.0 p_fbail1=2.0 p_loff=1E-6
  p_matrix=no p_c0=1/0 p_c1=0/1 p_rot=yes p_rotn="*1" p_sum=no
  p_product=no p_order=Rot+Sum+Product p_noescape=Off p_besquare=no
  p_srot=0.0 p_fixreflect=no p_icentre=0/0 p_iradius=2.0
  p_iiradius=1.0 p_rect=1.0 p_ode=no p_odestep=0.1/0.1 p_odeswitch=no
  p_os=none p_skip=1000.0 p_fix=no p_balance=1.0 p_maxhits=100.0
  p_count=100000.0 p_usemin=no p_minhits=2.0 p_col="#Hits/Iteration"
  p_iodepth=0 p_normalise=Off p_csel=Location p_acentre=0/0
  p_amethod="Centre Sum" p_aangle=Change p_atype="All Angles"
  p_auseall=no p_afade=0.9 p_adepth=3 p_aold=0 p_aselect=Max.
  p_arselect=Max. f_afn=ident p_ccentre=0/0 p_cmethod=Product
  p_cuseall=no p_cfade=0.9 p_cdepth=3 p_cold=0 p_cselect=Max.
  p_rselect=Max. f_cfn=ident p_mag=1.0 p_centre=0/0 p_formula=Henon
  p_one=1/1 p_mirax=1/-0.005 p_newrot=no p_a=1/0 p_b=1/0
  p_power=1.75/-0.5 p_power2=1/0 f_fn1=acos f_fn2=flip p_op=+ p_gdeg=2
  p_controlx="x:Const" p_controly="x:y coeff." p_degree=2
  p_control=Constant p_useroot=no p_root=1.55/-0.3 p_switch=1/0
  p_start=0.01/0 p_const=1/0 p_const1=-0.84615/-0.54438
  p_const2=1.47337/0.61538 p_const3=1/0 p_const4=1/0 p_const5=1/0
  p_const6=1/0 p_cg0=1/0 p_cg1=0/1 p_cg2=1/0 p_cg3=-1/0 p_cg4=0/0
  p_cg5=0/0 p_cg6=1/0 p_cg7=1/0 p_cg8=0/0 p_cg9=0/0 p_cg10=1/0
  p_cg11=1/0 p_cg12=0/0 p_cg13=0/0 p_cg14=0/0 p_cg15=1/0 p_cg16=1/0
  p_cg17=0/0 p_cg18=0/0 p_cg19=0/0 p_cg20=0/0 p_cg21=1/0 p_cg22=1/0
  p_cg23=0/0 p_cg24=0/0 p_cg25=0/0 p_cg26=0/0 p_cg27=0/0
inside:
  transfer=linear filename="mmf3.ucl" entry="MMF3-Periodicity"
  p_mode="True periodicity" p_colourby=Periodicity p_isolation=0
  p_fixval=yes p_usemin="Final z" p_method=Countdown p_count=1
  p_showall=yes p_frac=0.5 p_iter=50 p_colourmode=Original p_useall=no
  p_fixall=no p_colourall=no p_newfix=no p_threshold=1E-9 p_fill=Solid
  p_fillindex=1.0 p_smooth=None p_autopower=yes p_power=2/0
  p_bailout=65536.0 p_usefudge=no p_fudge=1.0 p_fudge1=1.0
  p_iterval=0.0 p_iterweight=50.0 p_logiter=Ident p_autopowerc=yes
  p_cpower=2/0 p_smallbail=1E-5 p_usefudgec=no p_fudgec=1.0
  p_fudge1c=1.0 p_fixedconv=no p_fixedval=1/0 p_itervalc=0.0
  p_iterweightc=50.0 p_logiterc=Ident p_zbasin=Off p_zscale=0.1
  p_convoff=0.0 p_mask=Off p_maskfirst=no p_mlow=0.1 p_mhigh=0.5
outside:
  transfer=linear filename="mmf4.ucl" entry="MMF4a-ForAttractors"
  p_version=1 p_method=Real
gradient:
  smooth=yes rotation=1 index=0 color=6555392 index=64 color=13331232
  index=168 color=16777197 index=257 color=43775 index=343 color=512
opacity:
  smooth=no index=0 opacity=255
}


The above is the Mandy for the standard Henon but with "self-rotation" added - this introduces *more* chaos which somewhat non-intuitively actually increases the chances of strange attractors !!
« Last Edit: October 19, 2012, 04:41:34 AM by David Makin » Logged

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David Makin
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« Reply #6 on: October 19, 2012, 04:47:19 AM »

Here's an orbit from that last Mandy - only parameters changed after switching are the max. iterations, inside colouring changed to black and the max. hits and max orbits parameters increased.....

Code:
Fractal2 {
fractal:
  title="Fractal2" width=928 height=696 layers=1
  credits="Dave Makin;10/19/2012"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=0/0 magn=1
formula:
  maxiter=1 percheck=off filename="Mmf4.ufm"
  entry="MMF4a-AttractorsPlus" p_version=3 p_mandy=no p_orbit=yes
  p_showinfo=yes p_julia=no p_progress=None p_bailtest=Both
  p_smallbail=1E-9 p_bailout=65536.0 p_lyapunov=no p_lbail=0.05
  p_lbail1=1.0 p_fdim=no p_fbail=0.0 p_fbail1=2.0 p_loff=1E-6
  p_matrix=no p_c0=1/0 p_c1=0/1 p_rot=yes p_rotn="*1" p_sum=no
  p_product=no p_order=Rot+Sum+Product p_noescape=Off p_besquare=no
  p_srot=0.0 p_fixreflect=no p_icentre=0/0 p_iradius=2.0
  p_iiradius=1.0 p_rect=1.0 p_ode=no p_odestep=0.1/0.1 p_odeswitch=no
  p_os=none p_skip=1000.0 p_fix=no p_balance=1.0 p_maxhits=900.0
  p_count=100000000.0 p_usemin=no p_minhits=2.0
  p_col="#Hits/Iteration" p_iodepth=0 p_normalise=Off p_csel=Location
  p_acentre=0/0 p_amethod="Centre Sum" p_aangle=Change
  p_atype="All Angles" p_auseall=no p_afade=0.9 p_adepth=3 p_aold=0
  p_aselect=Max. p_arselect=Max. f_afn=ident p_ccentre=0/0
  p_cmethod=Product p_cuseall=no p_cfade=0.9 p_cdepth=3 p_cold=0
  p_cselect=Max. p_rselect=Max. f_cfn=ident p_mag=1.0 p_centre=0/0
  p_formula=Henon p_one=1/1 p_mirax=1/-0.005 p_newrot=no p_a=1/0
  p_b=1/0 p_power=1.75/-0.5 p_power2=1/0 f_fn1=acos f_fn2=flip p_op=+
  p_gdeg=2 p_controlx="x:Const" p_controly="x:y coeff." p_degree=2
  p_control=Constant p_useroot=no p_root=1.55/-0.3
  p_switch=0.668462602/-0.5226361749 p_start=0.01/0 p_const=1/0
  p_const1=-0.84615/-0.54438 p_const2=1.47337/0.61538 p_const3=1/0
  p_const4=1/0 p_const5=1/0 p_const6=1/0 p_cg0=1/0 p_cg1=0/1 p_cg2=1/0
  p_cg3=-1/0 p_cg4=0/0 p_cg5=0/0 p_cg6=1/0 p_cg7=1/0 p_cg8=0/0
  p_cg9=0/0 p_cg10=1/0 p_cg11=1/0 p_cg12=0/0 p_cg13=0/0 p_cg14=0/0
  p_cg15=1/0 p_cg16=1/0 p_cg17=0/0 p_cg18=0/0 p_cg19=0/0 p_cg20=0/0
  p_cg21=1/0 p_cg22=1/0 p_cg23=0/0 p_cg24=0/0 p_cg25=0/0 p_cg26=0/0
  p_cg27=0/0
inside:
  transfer=none filename="mmf3.ucl" entry="MMF3-Periodicity"
  p_mode="True periodicity" p_colourby=Periodicity p_isolation=0
  p_fixval=yes p_usemin="Final z" p_method=Countdown p_count=1
  p_showall=yes p_frac=0.5 p_iter=50 p_colourmode=Original p_useall=no
  p_fixall=no p_colourall=no p_newfix=no p_threshold=1E-9 p_fill=Solid
  p_fillindex=1.0 p_smooth=None p_autopower=yes p_power=2/0
  p_bailout=65536.0 p_usefudge=no p_fudge=1.0 p_fudge1=1.0
  p_iterval=0.0 p_iterweight=50.0 p_logiter=Ident p_autopowerc=yes
  p_cpower=2/0 p_smallbail=1E-5 p_usefudgec=no p_fudgec=1.0
  p_fudge1c=1.0 p_fixedconv=no p_fixedval=1/0 p_itervalc=0.0
  p_iterweightc=50.0 p_logiterc=Ident p_zbasin=Off p_zscale=0.1
  p_convoff=0.0 p_mask=Off p_maskfirst=no p_mlow=0.1 p_mhigh=0.5
outside:
  transfer=linear filename="mmf4.ucl" entry="MMF4a-ForAttractors"
  p_version=1 p_method=Real
gradient:
  smooth=yes rotation=1 index=0 color=512 index=138 color=95 index=270
  color=43775 index=399 color=16777215
opacity:
  smooth=no index=0 opacity=255
}
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The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
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