In continiuing Lalla thread somewhere in parameters.
From mathematical point of view, in each iteration is added unit vector multiplied by some factor. What is unit vector one can read in wikipedia, but it seems that it helps formula to bail out sooner and substraction don't allows to bail out so soon.
http://en.wikipedia.org/wiki/Unit_vectorAs a result transformationr with positive factor shrunks all the fractals, and with a negative bloats them. This works in both 2D and 3D, there are some Ultra Fractal formulas using this transformation.
Transformation is from m3d version 1.8, throught here I used m3d version 1.7 so it could not work so, and deffinetely woun't work without _asdamTrans.m3f being copyed in respective folder.
example_1
Here I picked pretty basic Amazingbox with S = 2.5, min R =0.5, F=1.1 as a foundation.
Mandelbulb3Dv17{
Y.....S....O/...w....22...EMkif8KtM9.jHwsOJV4M5EyMxXLE0JkyHupsKxKYW9zonUsiCYc7.E
................................HyBHVzdzBz1........Y./..................y.2...rE
...Uz.....EV..../M.0/......v....p/....E3.....IYcOqiciBtD/..........m/dkpXm1....U
z.....kD12../..........wz..................................u1....y1...sD...../..
.z1...sDIwoAjGdPHyHpGk79UrhEy8NV61NA5Slj43W7DUB3erPkIZzuWuqYzMJDqmPQKzfjIg4fG4nV
Lw1q3BlMPNxjyke.Gq8ZiBtD......o8/.............sD.6....sD..kz....................
.............oAnAt1...sD....zU/SU6.is/W.MZ560UTSU6.au/W.sg560UxSU6......A....k1.
.....MEUZz1.......kz.wzzz1.U..6.P....E2...UD....m....c3....F....6/...I1.....SF5I
...U.qFG9yzb2zzzRYoWzz7lz16.oc..s5xd..kvrEtMc7xD/ocyFE0ujzH............B8..C6zA.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................wjXw.UvNPcveeWMW74.yRiibHJJ.U1n..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWMW74.IJ3.PlA.wyLsUa3f................................
E....2....E.....2....A....EEh3aSdtqNU6oPs/............................k/9.......
..................././........yDOaNaNaNalz1.....................................
................................................................................
........................}
example_2
The same Amazingbox, but after goes _asdamTrans with a scale 1. This is just an example of shrinkage, so must not be beautifull.
Mandelbulb3Dv17{
Y.....S....O/...w....22...EMkif8KtM9.jHwsOJV4M5EyMxXLE0JkyHupsKxKYW9zonUsiCYc7.E
................................HyBHVzdzBz1........Y./..................y.2...rE
...Uz.....EI..../M.0/.....k3/...o/....E3.....IYcOqiciBtD/..........m/dkpXm1....U
z.....kD12../..........wz..................................u1....y1...sD...../..
.z1...sDIwoAjGdPHyHpGk79UrhEy8NV61NA5Slj43W7DUB3erPkIZzuWuqYzMJDqmPQKzfjIg4fG4nV
Lw1q3BlMPNxjyke.Gq8ZiBtD......o00.............sD.6....sD..kz....................
.............oAnAt1...sD....zU/SU6.is/W.MZ560UTSU6.au/W.sg560UxSU6......B....k1.
.....MEUZz1.......kz.wzzz1.U..6.P....E2...UD....m....c3....F....6/...I1.....SF5I
...U.qFG9yzb2zzzRYoWzz7lz16.oc..s5xd..kvrEtMc7xD/ocyFE0ujzH............B8..C6zA.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................wjXw.UvNPcveeWMW74.yRiibHJJ.U1n..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWMW74.IJ3.PlA.wyLsUa3f................................
E....6....E.....2....A....EEh3aSdtqNU6oPs/............................k/9.......
..................././........yDOaNaNaNalz1.....................................
................................................................................
.....................2.....3....2....wJMnFKMhFZQVtqQ............................
4MU/..........................................................zD................
................................................................................
................................}
example_3
Then goes the same box, and the same transformation, but with negative scale -1. Amazing box now are bloated, and have more circles. If you cut this box you 'll notice hollows inside.
Mandelbulb3Dv17{
Y.....S....O/...w....22...EMkif8KtM9.jHwsOJV4M5EyMxXLE0JkyHupsKxKYW9zonUsiCYc7.E
................................HyBHVzdzBz1........Y./..................y.2...rE
...Uz.....kg..../M.0/......i....o/....E3.....IYcOqiciBtD/..........m/dkpXm1....U
z.....kD12../..........wz..................................u1....y1...sD...../..
.z1...sDIwoAjGdPHyHpGk79UrhEy8NV61NA5Slj43W7DUB3erPkIZzuWuqYzMJDqmPQKzfjIg4fG4nV
Lw1q3BlMPNxjyke.Gq8ZiBtD......oJ0.............sD.6....sD..kz....................
.............oAnAt1...sD....zU/SU6.is/W.MZ560UTSU6.au/W.sg560UxSU6......A....k1.
.....MEUZz1.......kz.wzzz1.U..6.P....E2...UD....m....c3....F....6/...I1.....SF5I
...U.qFG9yzb2zzzRYoWzz7lz16.oc..s5xd..kvrEtMc7xD/ocyFE0ujzH............B8..C6zA.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................wjXw.UvNPcveeWMW74.yRiibHJJ.U1n..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWMW74.IJ3.PlA.wyLsUa3f................................
E....6....E.....2....A....EEh3aSdtqNU6oPs/............................k/9.......
..................././........yDOaNaNaNalz1.....................................
................................................................................
.....................2.....3....2....wJMnFKMhFZQVtqQ............................
4MU/..........................................................zj................
................................................................................
................................}