ZBRUSH and MATHEMATICA

[cameyo]

Hi ZBrushers,
the following Alphas (grayscale images) are builted with "Wolfram Mathematica"....
The good (or bad) of these alphas is the precision...
They are built with mathematica formulas.
http://www2.zbrushcentral.com/zbc_uploads/user_image-1041272695ftz.jpg
ALPHA01
Mat1 =
1,1,1,1,1,1,1,1,1,1,
1,4,4,4,4,4,4,4,4,1,
1,4,7,7,7,7,7,7,4,1,
1,4,7,9,9,9,9,7,4,1,
1,4,7,9,0,0,9,7,4,1,
1,4,7,9,0,0,9,7,4,1,
1,4,7,9,9,9,9,7,4,1,
1,4,7,7,7,7,7,7,4,1,
1,4,4,4,4,4,4,4,4,1,
1,1,1,1,1,1,1,1,1,1
ListDensityPlot[mat1, Mesh -> False]

ALPHA02
DensityPlot[Sin[x*y]*Cos[x*y], {x, 0, 2*Pi}, {y, 0, 2*Pi}, Mesh -> False,
PlotPoints -> 1000]

ALPHA03
DensityPlot[Sin[x*y]*Cos[x*y], {x, -2*Pi, 2*Pi}, {y, -2*Pi, 2*Pi},
Mesh -> False, PlotPoints -> 1000]

ALPHA04
DensityPlot[x^2 + y^2, {x, -1, 1}, {y, -1, 1}, Mesh -> False,
PlotPoints -> 1000 ]

ALPHA05
DensityPlot[Sin[x]*Cos[y], {x, -1, 1}, {y, -1, 1}, Mesh -> False,
PlotPoints -> 1000 ]

ALPHA06
DensityPlot[Sin[x]*Cos[y], {x, -2*Pi, 2*Pi}, {y, -2*Pi, 2*Pi}, Mesh -> False,
PlotPoints -> 1000 ]

There are infinite possibilities...

If you don't like mathematica grab the alphas and use it !!!
DOWNLOAD: Alphas.zip (http://www2.zbrushcentral.com/zbc_uploads/user_file-1041272703rkj.zip)
I have the Notebook file used to built these alphas: i can send it to everyone who ask.

Another image:
http://www2.zbrushcentral.com/zbc_uploads/user_image-1041272934kpt.jpg
this image is the density plot of a special matrix: the solution matrix of a chess problem.
More than 200 years ago, Leonhard Euler posed the following problem:
Given a chessboard of n times n squares, is it possible to find a path for the knight that
touches every square exactly once in succession?
One alghoritm (not exact, but fast) was carry out by Warsndorff in 1820 ca.
I have implemented the Warsndorff alghoritm in Mathematica.
This is one matrix solution:
{" 1", "16", "39", "22", " 3", "18", "49", "56"},
{"38", "23", " 2", "17", "60", "55", " 4", "19"},
{"15", "40", "63", "54", "21", "48", "57", "50"},
{"24", "37", "42", "59", "64", "61", "20", " 5"},
{"41", "14", "53", "62", "47", "58", "51", "30"},
{"36", "25", "46", "43", "52", "31", " 6", " 9"},
{"13", "44", "27", "34", "11", " 8", "29", "32"},
{"26", "35", "12", "45", "28", "33", "10", " 7"}

I hope to have some time to do a more complex image with these ideas (Using AlphaCentury Technique and Make Alpha3D).
Ex. http://www2.zbrushcentral.com/zbc_uploads/user_image-1041273013gfo.jpg

p.s. Wolfram Mathematica is the top software on is category...(2200 euro)
It has many programming language built-in: Lisp-like, Prolog-Like, C-like,... www.wolfram.com (http://www.wolfram.com)

CIAO

Happy New Year to all

cameyo

[juandel]

http://www.cyber-webs.com/zbrush/juandel/cwa2.jpg

these are megacool alphas, cameyo! :tu:s to no end. mille gracie! manymany more of those, prego! happy calculating! :D

- juandel

[MrBraun]

Wauu bro !!! I haven't the word !!! :D
U are the 1^ person that use Mathematica in this easy way !!! :D
I have downloaded the demo... but..... mi mind crash... :D :D
Happy new year too buddy!!!!

[Flycatcher]

Well, there's a marriage I never expected to see - ZBrush and Mathematica! The mind boggles. :D :tu:

[cameyo]

Thank you all,
In the new year i'll post other of these alphas...they are a very pleasure to do.

Happy New Year

cameyo

p.s. Juandel: your images are truly unique and beatiful

[Frenchy Pilou]

Hi Cameyo
For the Knight travel, Take 64 different graduate levels of grey from start to the end ! You will obtain a 3D travel magic knight travel texture :)
May-be it's that you have made but I have not verify ! It'seems that there are more black squares ?
And if the square of start is the square of end, you will obtain a "closed travel" of knight.
But i don't remember if it's possible :)
Pilou Chess player