Custom formulas & transforms - WIP & discuss

[DarkBeam]

Need help; please go here http://www.fractalforums.com/new-theories-and-research/binary-box-tiling-(help-me!)/

ADDED Poincarè - now it is correct, previous version was wrong sorry.

[DarkBeam]

Added in final version spherical coord adjustment + an enhanced version of scaling that is useful for coordinate manipulation

[DarkBeam]

A "Sierpinski mandala", obtained with an angle multiplication, very similar to KPK formulas in UF (but in 3D!!!). This is only a quick example tough!

Mandelbulb3Dv16{
M.....S....O/...w....2.....fOPnJYIt/.jw0aqlz.62E5B9dSB1Ckv1012.MnU1wyk0agDfaADwD
................................Ctxd9Vwcoz1........Y./..................y.2.....
................/ME//....6U10...V1....E2.....wh70j0LxkqD/..........c./...w1.....
./EnAnYD..../..........wz.............................................sD...../..
.w1...sDPpngnwARcxXZpCK8Qp1Lzwe69s1.Oydj5o5alkJDQxffi4VBDH5Oz.MZNklOj1cjtFvJheY6
LuHi.Wof87mZyE2F3Q0LxkqD......2K......................sD..kz....................
.............................UJRR4.uppN.sNLb/UkRR4.arpN.cULb/U9SR4..............
...........................U..6.P....M4...EB....W....61....F....8/...I1....UJl12
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............28.kFrA0.
FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR
S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq
40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................
E....E....E.....I.........kLoxqQkVKNmZqMVl4.....................................
...................wz.........zD........kz1........wz...........................
................................................................................
.....................2.....3....2....wpIX34PdtqNklKRn/..........................
..............................zD........kz1........../........zD................
................................................................................
................................/....E/.........TZaPqB5QcJaQdBKMg/..............
..........U0............................U.2.....................................
................................................................................
..........................................k.....I....c....kIdJaQkZaPnhKOn.UQ....
..........................U/4MU/4M.................../........zD........kz1.....
...wz...........................................................................
........................................................}

[hobold]

"Ladies and gentlemen, fasten the seat-belts for take-off. We are now leaving solid mathematical ground and are headed for the utopia of artistic freedom."

Very good stuff! And my apologies for earlier derailing of this thread.

[bib]

"Ladies and gentlemen, fasten the seat-belts for take-off. We are now leaving solid mathematical ground and are headed for the utopia of artistic freedom."

You're late, buddy, it's been a year since I don't touch the ground anymore  :

[DarkBeam]

  Hi and thanks to everybody who posted encouraging comments! I don't have the material time to thank everybody singularly but keep doin!
Sometimes fractals do bad jokes to me! I tested tospherical and invspherical with Menger3 and Sierpinski and it worked well. But testing with integer power shows an effect similar to "conj" formula ... Not good definitely!

Due to bad coding, invspherical do also a flipxy, and it is not wanted! So I have to fix again! (download again final.zip)

[bib]

Luca. Take your time. No rush In fractals, quality is better than quantity

[DarkBeam]

Luca. Take your time. No rush In fractals, quality is better than quantity

If only I was sage!
Uploaded new transforms for toric space; inversions are NOT correct but they give funny results.  I don't know the correct formula, anyone???

[DarkBeam]

Released a Barnsley in 4 dimensions and a box tiling. The box tiling gives incredible effects when combined with Amazing box & c.

[bib]

Please stop Luca !! I don't have the time to test

[lenord]

I keep downloading them just to stay current but haven't had the time to try more that a couple of them. Too many toys too little Playtime.

[DarkBeam]

Please stop Luca !! I don't have the time to test

This new world awaits you. Don't you want to get in the forest?

[DarkBeam]

Mandelbulb3Dv16{
M.....S....O/...w....2.............6.1.......s3E................................
.....................UF92FpyVYzD8QxckpX05z1........Y./..................y.2.....
................/ME//....6U./...f/....E2.....Qz/NcmCAZtD/..........c./...w1....U
z.....kD..../..........wz.............................................sD...../..
.w1...sDYsAIxzzzjz1..........WAbUdisqcljTcFzUvMS3t97C1JzzzzvzUNehUisqcljMaO9c9iB
Ow1mQ0auWPX4zU2bVezzzzyD......22......................sD..kz0...................
.............................UJRR4.uppN.sNLb/UkRR4.arpN.cULb/U9SR4..............
...........................U..6.P....M4...EB....W....61....F....8/...I1....UJl12
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............28.kFrA0.
FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR
S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq
40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................
E....6....E.....I....E....kLWx4SoZ4PdtqN........................................
...................0./.......U.E..........UNaNaNaNaxz...........................
................................................................................
.....................Uy....3....4....2YEjVbJV7LSHBKMgJ4BY/......................
.Q...2.......................U.E........Uz1........wz...................kz1.....
................................................................................
................................}

 

[DarkBeam]

Added the non-commutative (Hamiltonian) version of the Barnsley formula. It looks more roundy.

The strange thing is that commutative Barnsley has a beautiful mset and "flat" Julia while the noncommutative has a beautiful Julia and awful mset

[DarkBeam]

Added too Barnsley2 variations comm & non comm, Barnsley2 shares 80% of the code with his brother