Logo by bib - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Check out the originating "3d Mandelbulb" thread here
 
*
Welcome, Guest. Please login or register. March 19, 2024, 03:40:59 AM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Pages: [1]   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: syerpinsky carpets and cellular automatas applied at Cross method  (Read 408 times)
Description: wonder of physics
0 Members and 1 Guest are viewing this topic.
hgjf2
Fractal Phenom
******
Posts: 456


« on: May 19, 2016, 09:59:28 PM »

If you using cross method for calculus the structures statical undetermined or for approximated at plates calculus (applying the biharmonical equation
[(df^2/d^2x)+(df^2/d^2y)]^2=a, where a=1 if x=0 and y=0 and a=0 if x<>0 or y<>0. If approximating formulas and taking last digit of integer part. This grid look like a automata cellular if the structures have infinity grid.

Logged
hgjf2
Fractal Phenom
******
Posts: 456


« Reply #1 on: May 19, 2016, 10:11:30 PM »

If you using cross method for calculus the structures statical undetermined or for approximated at plates calculus (applying the biharmonical equation
[(df^2/d^2x)+(df^2/d^2y)]^2=a, where a=1 if x=0 and y=0 and a=0 if x<>0 or y<>0. If approximating formulas and taking last digit of integer part. This grid look like a automata cellular if the structures have infinity grid.


For to using Cross's method for the differential eqution of the biharmonicity must using: f(x-2;y)-8*f(x-1;y)+20*f(x;y)-8*f(x+1;y)+f(x+2;y)+2*f(x-1;y-1)-8*f(x;y-1)+2*f(x+1;y-1)+2*f(x-1;y+1)-8*f(x;y+1)+2*f(x+1;y+1)+f(x;y-2)+f(x;y+2)=P where P is the force applied on the plate at the point (x;y).
If adding new condition , as example like f(5;y)=0 with f(-5;y)=0 with f(x;7)=0 with f(x;-7)=0 then the infinity matrix of the values f(x;y) that x and y are integer numbers look like a automata cellular and like a fractal persan carpet for P=1 when x=0 and y=0 else P=0. Let's try this on MATHCAD.

« Last Edit: May 19, 2016, 10:17:51 PM by hgjf2 » Logged
hgjf2
Fractal Phenom
******
Posts: 456


« Reply #2 on: May 24, 2016, 09:16:57 AM »

An example of so infinity matrix whick using the biharmonicity equation but for the calculus of efforts for a board suppossed at vibration is:

    -1    ;0    ;0    ;0    ;0    ;0    ;0    ;...
     3    ;1    ;0    ;0    ;0    ;0    ;0    ;...
     24   ;-2   ;-1   ;0    ;0    ;0    ;0    ;...
     -64  ;-8   ;1    ;1    ;0    ;0    ;0    ;...
     0     ;0    ;0    ;0    ;-1   ;0    ;0    ;...
     64   ;8    ;0    ;0    ;-1   ;1    ;0    ;...
     424  ;0   ;8   ;0     ;8     ;2    ;-1  ;...
.............................................................
 this is only a part of this infinity matrix
Logged
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #3 on: May 24, 2016, 12:35:41 PM »

This looks interesting but I cannot understand you! sad
Please can you explain step by step how you mix matrix... differential equations ... and finally the automatas?
Those concepts are so distant that I just cannot imagine how to mix em embarrass
Logged

No sweat, guardian of wisdom!
hgjf2
Fractal Phenom
******
Posts: 456


« Reply #4 on: May 25, 2016, 09:53:47 AM »

This looks interesting but I cannot understand you! sad
Please can you explain step by step how you mix matrix... differential equations ... and finally the automatas?
Those concepts are so distant that I just cannot imagine how to mix em embarrass
This part of the infinity "carpets" of number not need an differential equation. Just applying only the formula f(x-2;y)-8*f(x-1;y)+
20*f(x;y)-8*f(x+1;y)+f(x+2;y)+2*f(x-1;y-1)-8*f(x;y-1)+2*f(x+1;y-1)+2*f(x-1;y+1)-8*f(x;y+1)+2*f(x+1;y+1)+
f(x;y-2)+f(x;y+2)=0

The ordering is:   
                            1
                        2; -8; 2
                     1;-8;20;-8;1
                         2;-8; 2
                             1
     is just numerical interpolation for equation ((d2f/dx2)+(f2f/dy2))^2=0 the biharmonical equation.
Logged
Pages: [1]   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
Cellular automatas Mathematics « 1 2 » matsoljare 18 14505 Last post March 17, 2015, 11:54:04 AM
by jehovajah
Mandelbox folding applied to a Julibrot 3D Fractal Generation David Makin 2 3922 Last post March 16, 2010, 05:35:00 AM
by Timeroot
Mandelbox folding applied to a quaternion 3D Fractal Generation David Makin 8 4441 Last post March 18, 2010, 07:18:42 PM
by kram1032
fractal homeomorphisms applied to Lena Introduction to Fractals and Related Links louisa 1 1782 Last post March 03, 2012, 06:44:48 AM
by Dinkydau
Flying Carpets in the Wild Mandelbulber Gallery mclarekin 0 381 Last post May 16, 2014, 12:42:45 PM
by mclarekin

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.137 seconds with 24 queries. (Pretty URLs adds 0.005s, 2q)