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Author Topic: help on finding classic fractals in -1.5 mandelbox  (Read 3010 times)
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cKleinhuis
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« on: October 10, 2012, 04:46:45 PM »

hi there,

perhaps i am faster with your help, i would like to render examples of the standard fractals that can be found in the mandelbox scale -1.5

like miqel collected on his page :

http://www.miqel.com/fractals_math_patterns/mandelbox_3d_fractal.html

any help with mandelbulb formula files are appreciated, i want to use them in my forthcoming speech, the corner object is easy to find wink

where to find the sierpinski gasket, the trees, the mengers ?!?!?

Mandelbulb3Dv18{
b.....S....O/...w....2.....2b98py18..5hm3GO0DAzjMsCAolRfzzXKK8fu0bvzz2r.nQ3d.zzj
................................vGVTp2HF3/2........Y./..................y.2...wD
...Uz.....E2..../M.0/......X/...v2....E3.....IdP8C/2bhlD/..........m/dkpXm1.BnAn
x.....kD12../..........wz..................................u1....y1...sD...../..
.z1...sD7RTDF.lNPw1..........OcLLiIjmNYjcX8kOZYnzsnesC.ITQp2z.f8CG2edBlDKIJbpgyf
zsHEBwWFcaq2zC0NYto5LBlD......2B..............sD.6....sD..E.0...................
.............oAnAt1...sD....z.Lv.A.2i1k.kuC.1.pv.A.wj1k.E0D.1.Hw.A......Z....k1.
..................kz.wzzz1.U..6.P....U5...EB....m....c3....3....6/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD4ocyFE0ujz1..........2.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E....2....E.....2....A....EEh3aSdtqNU6oPs/UQ..........................k/9.......
...................yz0........yD........kz1.....................................
................................................................................
........................}


* mandelbox.jpg (88.04 KB, 480x360 - viewed 568 times.)
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Madman
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« Reply #1 on: October 10, 2012, 09:54:40 PM »

Interesting challenge, Christian. I've found a fractal tree here:

Mandelbulb3Dv18{
b.....Y/...g2...w....26...UN6Esp2/3zzyrgcaQCcjzjvkv8uozquzXpcsmhDyTyzA7YsnUN/lzj
................................EEJFsQNCF02........Y./..................y.2...wD
...Uz.....U8..../MU0/.....kS2...B4....E3.....UaJrKTWBFfD/..........m/dkpXm1.OaNa
z.UaNadD12..0..........wz..................................u1....y1...sD...../..
.z1...kD6yI0Hz4iEu9AfOdhVzkgyWrU1w0XbNdD1gG7ULOgYu1h6FsqJNyay8C6tKgy1.fjFtYvD3Ux
kuXdjrGy.W3Lyy2hLrP6BNeD......ol/.............sD.6....sD..E.....................
.............oAnAt1...sD....z.Lvl9.2i5j.kuSw0.pvl9.wj5j.E0Tw0.Hwl9......d....k1.
.....AQxcz1.......kz.wzzz1.U..6.P....U5...EB....m....c3....3....6/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD4ocyFE0ujz1..........2.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E....2....E.....2....A....EEh3aSdtqNU6oPs/UQ..........................k/9.......
...................yz0........yD........kz1.....................................
................................................................................
........................}


* mandelbox_tree.jpg (162.47 KB, 800x600 - viewed 62 times.)
« Last Edit: October 10, 2012, 10:21:08 PM by cKleinhuis, Reason: added rendering » Logged

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cKleinhuis
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« Reply #2 on: October 10, 2012, 10:08:55 PM »

great starter, thank you for that  embarrass, thought it had mengers on its top wink but didnt  hurt,


found until now:

- Poincare Disks & Hyperbolic Tilings ( behind Apollony fractal in corner! )
- Apollony Fractal
- fractal tree

who finds ( at best in the -1.5 box )

-Koch Curve    
-Cesaro Curve & Koch Inversions      
-Koch Snowflake      
-Dense Fractal Branching Structures  
-Sierpinski Triangles
-Menger Sponge / Sierpinski Carpet Hybrid    
-IFS & L-System Fractals

just a list from the miqels site, just amazing what all is hidden inside the -1.5 box !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! woot woot!
 afro
« Last Edit: October 10, 2012, 10:21:55 PM by cKleinhuis » Logged

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Madman
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« Reply #3 on: October 10, 2012, 10:22:46 PM »

I think I've found a menger sponge like thing:

Mandelbulb3Dv18{
b.....Y/...g2...w....26...kMj26CdDtzzezmckxKmqzjsvlW4OewtzXMA7/LczAzzwAhIr75cxzj
................................ohnn2O4Nr/2........Y./..................y.2...wD
...Uz.....UJ..../MU0/.....kK/...O4...2E3.....geTtj7SargD/..........m/dkpXm1.OaNa
z.UaNadD12..0..........wz..................................u1....y1...sD...../..
.z1...kDf7YqtuSUAv1mUCEfgiRgyYAuPV9cOFcj2FBEuAfAkuv.onM2.nrlyUtBoOEzW0gjAeP58Z2k
TufAtg2/GH1kyAzt4JqpDXgD......Iy..............sD.6....sD..E.....................
.............oAnAt1...sD....z.Lvl9.2i5j.kuSw0.pvl9.wj5j.E0Tw0.Hwl9......e....k1.
.....AQxcz1.......kz.wzzz1.U..6.P....U5...EB....m....c3....3....6/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD4ocyFE0ujz1..........2.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E....2....E.....2....A....EEh3aSdtqNU6oPs/UQ..........................k/9.......
...................yz0........yD........kz1.....................................
................................................................................
........................}


* mengercandidate.jpg (73.21 KB, 800x600 - viewed 59 times.)
« Last Edit: October 10, 2012, 10:34:47 PM by cKleinhuis, Reason: added rendering » Logged

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cKleinhuis
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« Reply #4 on: October 10, 2012, 10:29:16 PM »

lol, naa, not original mengerish, but you found the lsystem ifs like patterns on the sides of that plane, lol, browsing around and found what i expected on the first tree:

Mandelbulb3Dv18{
b.....m....K0...w....26...k5hvSnXjtzzGL6XWo/Oyzj/Joew3huuzHe6sM8a09zzIu1EA/jPyzj
................................1bj1x/Qmt12........Y./..................y.2...wD
...Uz.....E2..../MU0/.....EW1...m5...2E3.....Um1JN5ITgZD/..........G/dkpXm1.OaN4
z.UaNadD12../..........wz..................................u1....y1...sD...../..
.z1...kD2nvR2sEW0tP2o/LVsXkEy.XldMqQZSZDc89ufdWd4sPeo1q0FsEKyMsSZuiGtGYjI6rcrzhS
Ntfp6Vnx148AyuoNbiwAU0Yj......Yr..............sD.6....sD..E.0...................
.............oAnAt1...sD....z.rbu3.2UeL.k0eS/.Jcu3.wVeL.E8eS/.ncu3......n....k1.
.....AQxcz1.......kz.wzzz1.U..6.P....U5...EB....m....c3....3....6/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD4ocyFE0ujz1..........2.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E....2....E.....2....A....EEh3aSdtqNU6oPs/UQ..........................k/9.......
...................yz0........yD........kz1.....................................
................................................................................
........................}


* mandelbox_tree_ifs_lsystem.jpg (153.38 KB, 800x600 - viewed 65 times.)
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ericr
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« Reply #5 on: October 10, 2012, 10:33:00 PM »

sorry I dont find the Poincare Disks & Hyperbolic Tilings ( behind Apollony fractal in corner! )
erircr
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Madman
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« Reply #6 on: October 10, 2012, 11:22:30 PM »

Well, to me it looks the same as what Miqel calls a Menger / Sierpinski hybrid:

Still enjoying the journey btw, now looking for the elusive Sierpinski triangles...
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cKleinhuis
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« Reply #7 on: October 10, 2012, 11:31:33 PM »

yay, thanks madman, it is the menger structure miqel meant, great, i even found something that remindet me to the original set, at least the arrangement of circles somewhere near that

 @eric they are on the square at the corners and all around, hard to see but they are there, depending on the light and color setup, beside of that some of them are capped and just flat, try going on the other side of the cube then wink
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Tglad
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« Reply #8 on: October 11, 2012, 12:17:58 AM »

Koch snowflakes are on the face of the corner box. You can see them small in the first picture here:
https://sites.google.com/site/mandelbox/negative-mandelbox
The Masket fractal (lower down) is under 'the bridge' on the Mandelbox edge, and offset to each side.

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marius
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« Reply #9 on: October 11, 2012, 07:34:33 AM »

Fun hunt

Here are a couple of snapshots taken flying around w/ boxplorer2. Seems the familiar forms are indeed near the corners.

https://picasaweb.google.com/106319810259021598504/Mbox155?authkey=Gv1sRgCKG5x4fs8LyJvAE
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cKleinhuis
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« Reply #10 on: October 11, 2012, 10:30:40 AM »

@tglad i am unsure how to interpret your description, with corner box you mean the tiny boxes at the borders ?!
lol, it might be that i oversaw the koch kurve, have not found a good looking example yet, at least i have not seen it

if you have the time would be great to have mb3d locations for them ... wink for sure i am going to make a video out
of it sometime, a trip to all common structures in the box!

thanks for helping, will have another look tonight!
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KRAFTWERK
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« Reply #11 on: October 11, 2012, 11:58:59 AM »

Had to go on treasure hunt...  afro
Found this:

Mandelbulb3Dv18{
b....ET....x/...w....2.....yrePKbZVzzu7Ckx3ClHzjRCQ9YUJYvznLinxtllJYzcNC6bKMKszj
................................2eIkQvfxr02........Y./..................C/2...wD
...Uz.....U1..../M.0/.....Ey....M3...2E3......sY0nsTNReD/.......bJ3o/dkpXm1.lJJp
z.....kD12../..........wz..................................u1....y1...sD...../..
.z1...sDO2PB/fSmSunc2SlM85.UyQ09bPy805fjduthSWVbUu9g2j4lrHMgyYPvzAHo7cbjAWMNogAd
juHka7HNXE5cy.u6zDpWXwdD......o3..............sD.6....sD..E.....................
.............oAnAt1...sD....z.rbu4.2UeP.k0ei/.Jcu4.wVeP.E8ei/.ncu4......X....k1.
..................kz.wzzz1.U..6.P....w4...EB.........c3...ED....5/...I1.....SF52
...U.ydelyjeYFnzTeOgzf8No.6.nc...1Ak..E92FpyVYyD4wXl59h0Bz9...........k.8.kXWF1.
.sM93P58iz9.MmnWK2zwz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1....................................uBZ.U7EgU7zzFoTu2.oQm2oszDnueM.YXB
bYHzTt6Ul/k6Ukl6Qs5crI0.a.l0a.bTUSH7.M029M0ly/uBZ.U7EgU7Mw5crI0.a.l0akqTUSH7.M02
9M0kz/uBZ.U7EgU7...crIGJzzFoTuIdyzngi8qdxzZX.4rU................................
E....2....E.....2....A....EEh3aSdtqNU6oPs/UQ..........................k/9.......
...................yz0........yD........kz1.....................................
................................................................................
........................}


* 4Kleinhaus.jpg (128.05 KB, 500x500 - viewed 525 times.)
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cKleinhuis
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« Reply #12 on: October 11, 2012, 01:32:26 PM »

cool, thx, the name amazing box is so much suitable, if anyone has concrete params for other types, please post em

regards all! tomorrow i am going on my trip to mexico!
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divide and conquer - iterate and rule - chaos is No random!
cKleinhuis
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« Reply #13 on: October 11, 2012, 02:07:47 PM »

@tglad, what do you mean with "face of the corner box" ?!? each side of the corner box has a circle, but where is the koch kurve in this circle ?!?!??!
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divide and conquer - iterate and rule - chaos is No random!
cKleinhuis
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« Reply #14 on: October 11, 2012, 02:44:09 PM »

what side do you exactly mean ?!? huh?

when i travel into the center of the boxes, i find mostly square structures like this, but no koch flakes sad your image seems to go out of the face, my face centers always point inside the boxes ....  sad

Mandelbulb3Dv18{
b.....S....O/...w....2....knVzqpk1uzzitnbRBwUyzjezggik6czzH.DvLtzzzzzYJPjRBwUyzj
................................php5O/3aV72........Y./..................y.2...wD
...Uz.....k3..../M.0/.....kB/...i6....E3.....cPP2/fAE0ED...........m/dkpXm1.BnAn
x.....kD12../..........wz..................................u1....y1...sD...../..
.z1...sDxvpWYmHXenfFF/3Mg1HzweCnudgxQ0CDushO7DpPan1VhEgpmaYuwuLc5sFC1lDjsKfbJkqA
wn1tof5z9QEsw0hhiTZ/CtCD......2I..............sD.6....sD..E.0...................
.............oAnAt1...sD....z.Lvi9.2ivi.kuiv0.pvi9.wjvi.E0jv0.Hwi9......w....k1.
..................kz.wzzz1.U..6.P....U5...EB....m....c3...E4....6/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16/pE/.zXCc..UmN80.6FwD4.o1a.hW0.2.EPcQjRTzz4.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E....2....E.....2....A....EEh3aSdtqNU6oPs/UQ..........................k/9.......
...................yz0........yD........kz1.....................................
................................................................................
........................}


* centerface.jpg (50.15 KB, 480x360 - viewed 500 times.)
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divide and conquer - iterate and rule - chaos is No random!
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