Title: syerpinsky carpets and cellular automatas applied at Cross method Post by: hgjf2 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. Title: Re: syerpinsky carpets and cellular automatas applied at Cross method Post by: hgjf2 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 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).[(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. 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. Title: Re: syerpinsky carpets and cellular automatas applied at Cross method Post by: hgjf2 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 Title: Re: syerpinsky carpets and cellular automatas applied at Cross method Post by: DarkBeam on May 24, 2016, 12:35:41 PM This looks interesting but I cannot understand you! :sad1:
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: Title: Re: syerpinsky carpets and cellular automatas applied at Cross method Post by: hgjf2 on May 25, 2016, 09:53:47 AM This looks interesting but I cannot understand you! :sad1: 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)+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: 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. |