Title: Another shot at the holy grail Post by: quick-dudley on November 06, 2012, 03:36:22 AM I forget what inspired me to do away with i, but here's the basic result:
(http://nocache-nocookies.digitalgott.com/gallery/12/7907_06_11_12_3_16_48.jpeg) It uses two pseudo-imaginary numbers which follow this multiplication table:
For: For a number space that doesn't use i, it's a surprisingly natural three dimensional generalisation of complex numbers The cross-section y=z is the mandelbrot set (although slanted) Some areas are complex and compelling even outside the cross-section y=z Against: Some surfaces are too smooth. Some areas look like candyfloss It is not symmetrical. Here is another view... (http://nocache-nocookies.digitalgott.com/gallery/12/7907_12_11_12_5_58_15.jpeg) Title: Re: Another shot at the holy grail Post by: DarkBeam on January 23, 2015, 12:25:01 PM Is someone able to convert it to a squaring rule?
Like... Nx= x^2-y^2+cx Ny=xy+cy ... Luca :D Title: Re: Another shot at the holy grail Post by: lkmitch on January 23, 2015, 04:44:16 PM It uses two pseudo-imaginary numbers which follow this multiplication table:
1 m n 1 1 m n m m n -1 n n -1 m If T = x + ym + zn, then T^2 = (x + ym + zn)*(x + ym + zn) = x^2 + xym + xzn + xym + y^2m^2 + yzmn + xzn + yzmn + z^2n^2. Using the multiplication table, T^2 = x^2 - 2yz + m(2xy + z^2) + n(-2xz + y^2) real part: x^2 - 2yz m part: 2xy + z^2 n part: -2xz + y^2 Title: Re: Another shot at the holy grail Post by: DarkBeam on January 24, 2015, 10:54:46 AM Thanks dear sir :beer: :beer:
Title: Re: Another shot at the holy grail Post by: youhn on January 25, 2015, 01:08:33 PM Is this correct?
Code: double x2 = z.x * z.x; Some images of rotating around it: (http://i.imgur.com/vV40Uaz.png) (http://i.imgur.com/y5aoorn.png) (http://i.imgur.com/MHRVmiY.png) (http://i.imgur.com/2io7YtF.png) (http://i.imgur.com/v8lpkcP.png) (http://i.imgur.com/YF7dBS0.png) (http://i.imgur.com/khV6Iln.png) (http://i.imgur.com/JSc39v6.png) (http://i.imgur.com/RSUpmSs.png) (http://i.imgur.com/Jun9L6b.png) (http://i.imgur.com/rBEoNEY.png) (http://i.imgur.com/D70z1Ux.png) (http://i.imgur.com/kIXQNbH.png) (http://i.imgur.com/lmj8nlT.png) (http://i.imgur.com/Irx5SGI.png) (http://i.imgur.com/cUkOrx3.png) Created with hacked version of Mandelbulber v2.02. Title: Re: Another shot at the holy grail Post by: youhn on January 25, 2015, 01:57:24 PM After comparing the images, it does NOT seem to be the same thing. Is it a mistake to map the Re, m, n parts to X, Y, Z axis in Mandelbulber?
{additional edit} It has celtic cross like structures: (http://i.imgur.com/cQXoDHR.png) Title: Re: Another shot at the holy grail Post by: eiffie on January 25, 2015, 04:32:00 PM From the multiplication table I get newz=2*x*z+y^2 but I like the celtic crosses so I left it as -2*x*z in this webgl animation thingy...
https://www.shadertoy.com/view/MtsGD4 (https://www.shadertoy.com/view/MtsGD4) Title: Re: Another shot at the holy grail Post by: DarkBeam on January 25, 2015, 04:44:12 PM Just noticed this fmla is 3 years old!
Then go digging again! :D Title: Re: Another shot at the holy grail Post by: DarkBeam on January 25, 2015, 04:51:41 PM I wonder if it's raelly worth it to implement since there's already a "Makin3D-2" formula in MB3D almost identical;
x' = +x*x + z*y*2 + Cx y' = -y*y - z*x*2 + Cy z' = -z*z + x*y*2 + Cz Title: Re: Another shot at the holy grail Post by: DarkBeam on January 25, 2015, 05:20:49 PM Yeah I implemended Kerry Mitchell's formula and the correct one. Awesome teamwork thanks :beer:
Param showing a crossy Julia; Mandelbulb3Dv18{ g.....S....O/...w....2....kpdAwlMZd0.9IgT8dZ/f1EuOFyVBMV.wP2eBq7ubRqzU2przhyeExj ................................psPTcndFpz1........A./..................y.2...wD ...Uz6.....0..../M.0/.....EN/...U/....E3.....AIEqGuCZhqD/..........m/dkpXm1....U z.EnAnYD12../2Exo8FPArVzzmgFFK4dHmpDeQH9kORsax9...........U0.....y1...sD...../.. .zXaNadDs2TOWiHNfx1..........SSDKsMDlNdjSQ4Rz.cM0r9ClbacvIqOzwwGokMDlNdjFj2BAqHQ KunuxMVXx2bZy.HcR.uCZhqDU.....Y5..............sD.6....sD..G..................... .............oAnAt1...sD....z...........................................C....k1. .....Ksulz1.......kz.wzzz1.U..6.P....U5...EB....m....c3....F....6/...I1.....SF52 ...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD6ocyFE0ujz1..........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..F2E.....I.........EIpZqMfFIRYlKNthIH.........................c.......... ...................6./........zj................................................ ................................................................................ ........................} {Titel: Crosses in KM~} In the "correct brot" you may find nice spots near the minibrots Mandelbulb3Dv18{ g.....m....V1...w....2....UYsOp7DW1ozWzGNzwA5Z0EsCl1eu2ivzfbvek7PA5VzSiFJFK5MUuj ................................OFjP0RNKr.2........A./..................y.2...wD ...Uz6........../M.0/.....UE/...r/....E3.....UawVZ0IorlD/.......nee70dkpXm1....U z.UaNaVD12../.Exo8FPArVzzmgFFK4dHmpDeQH9kORsax9...........U0.....y1...sD...../.. .zXaNadDr.jvP05lsvHOD6zrh6Y3z.wdVGcgEAljqN4wrKQUvv9ko/55Zi.3z.03KBiOfIlD26Z1llHT QwnikXxIJHZ9yEg58gQo/8kDU.....o6..............sD.6....sD..G..................... .............oAnAt1...sD....z...........................................O....k1. .....Ksulz1.......kz.wzzz1.U..6.P....U5...EB....m....c3....F....6/...I1.....SF52 ...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD6ocyFE0ujz1..........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..F2E.....I.........EIpZqMfFIRYlKNt/EH.........................c.......... ...................6./........zj................................................ ................................................................................ ........................} {Titel: Minibrots~} Cool spirals (in 3D) in a Julia: Mandelbulb3Dv18{ g.....m....V1...w....2....k.dNtrZgc/.940MsEjO41EAT2qgukKHz99VgLDbUjYzsWtG/C.Gmwj ................................oAeYyethxz1........A./..................y.2...wD ...Uz6.....A..../M.0/.....ET0...u/....E3.....wngt3gG7SpD/.......nee70dkpXm1....U z.UaNaVD12../2...........cNaNaNaNavj........Uz9...........U0.....y1...sD...../.. .zXaNadDrrh7esSRnw1/xxtx5pLIzYd9yc3uprojDzcjNuDbpwPuyWO82/sHz.OaieoDW0pDfI4IHFdM Kx1y0WLhVIxNysSNWQBMJonDU.....I./.............sD.6....sD..G..................... .............oAnAt1...sD....z...........................................M....k1. .....Ksulz1.......kz.wzzz1.U..6.P....U5...EB....m....c3....F....6/...I1.....SF52 ...U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc..kvrEtMc7xD6ocyFE0ujz1..........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..F2E.....I.........EIpZqMfFIRYlKNt/EH.........................c.......... ...................6./........zj................................................ ................................................................................ ........................} {Titel: Spirals} Title: Re: Another shot at the holy grail Post by: youhn on January 26, 2015, 07:18:56 PM Here's a picture from the correct formula from quick-dudley :
(http://i.imgur.com/zTt3AKD.jpg) Created with slightly altered version of Mandelbulber v2.02. Title: Re: Another shot at the holy grail Post by: youhn on January 28, 2015, 11:23:29 PM Another one from the quick-dudley version. A 3D julia.
(http://fc02.deviantart.net/fs71/i/2015/028/9/f/filament_cleaning_ship_by_jeroensnake-d8frxf5.png) Source: http://jeroensnake.deviantart.com/art/Filament-cleaning-ship-510226673 Title: Re: Another shot at the holy grail Post by: matsoljare on January 29, 2015, 07:38:31 PM Whoa, let's see that one rotated....
Title: Re: Another shot at the holy grail Post by: youhn on January 30, 2015, 07:49:56 PM Rotated or rotating? The first I actually rendered before the one above, but I didn't like the colors. If you mean rotating as in animated ... don't count on me. My expectations of image quality do not (yet) match with my patience and computational speed of computers.
(http://i.imgur.com/AQxgMrw.jpg) Not sure if this is the exact same location. Rotation 45 deg, roll of 90 deg. Title: Re: Another shot at the holy grail Post by: Alef on January 31, 2015, 03:32:07 PM Cool visuals but no. Too stretched.
Title: Re: Another shot at the holy grail Post by: eiffie on January 31, 2015, 04:09:42 PM Perfect render but it looks like it won't hold still for the camera :) |