Chaos blog

Monday, April 16, 2012

3-cells CNN

3-cells CNN chaotic system

3-cells CNN chaotic system for arduino with gameduino shield.

http://www.mathworks.com/matlabcentral/fileexchange/27336-fractional-order-chaotic-systems

http://www.arduino.cc/

http://excamera.com/sphinx/gameduino/

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#include "SPI.h"

#include "GD.h"

byte i;

float p1 = 1.24;

float p2 = 1.1;

float r = 4.4;

float s = 3.21;

float h1 = 0;

float h2 = 0;

float h3 = 0;

float x = 0.1;

float y = 0.1;

float z = 0.1;

float xn = x;

float yn = y;

float zn = z;

float dt = 0.01;

void setup()

{

GD.begin();

GD.ascii();

GD.wr16(RAM_SPRPAL + (0 * 2), 0x8000);

GD.wr16(RAM_SPRPAL + (1 * 2), RGB(255, 255, 255));

GD.fill(RAM_SPRIMG, 0, 256);

GD.wr(RAM_SPRIMG + 0x78, 1);

GD.putstr(12, 1, "3-Cells CNN chaotic system");

}

void loop()

{

h1 = 0.5*(abs(x+1)-abs(x-1));

h2 = 0.5*(abs(y+1)-abs(y-1));

h3 = 0.5*(abs(z+1)-abs(z-1));

xn = -x+p1*h1-s*h2-s*h3;

yn = -y-s*h1+p2*h2-r*h3;

zn = -z-s*h1+r*h2+h3;

x = x+xn*dt;

y = y+yn*dt;

z = z+zn*dt;

GD.sprite(i++, 200+(105*x), 150+(95*y), 0, 0, 0);

}

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Sunday, March 18, 2012

Arneodo

Arneodo chaotic system

Arneodo chaotic system for arduino with gameduino shield.

http://www.scientific.net/AMM.130-134.2550

http://www.arduino.cc/

http://excamera.com/sphinx/gameduino/

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#include "SPI.h"

#include "GD.h"

byte i;

float a = -5.5;

float b = 3.5;

float c = -1;

float x = 0.1;

float y = 0;

float z = 0;

float xn = x;

float yn = y;

float zn = z;

float dt = 0.009;

void setup()

{

GD.begin();

GD.ascii();

GD.wr16(RAM_SPRPAL + (0 * 2), 0x8000);

GD.wr16(RAM_SPRPAL + (1 * 2), RGB(255, 255, 255));

GD.fill(RAM_SPRIMG, 0, 256);

GD.wr(RAM_SPRIMG + 0x78, 1);

GD.putstr(14, 1, "Arneodo chaotic system");

}

void loop()

{

xn = y;

yn = z;

zn = -a*x-b*y-z+c*pow(x,3);

x = x+xn*dt;

y = y+yn*dt;

z = z+zn*dt;

GD.sprite(i++, 200+(50*x), 152+(20*y), 0, 0, 0);

}

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Saturday, March 17, 2012

Ikeda

Ikeda chaotic attractor

Ikeda chaotic attractor for arduino with gameduino shield.

http://www.bentamari.com/attractors.html

http://www.arduino.cc/

http://excamera.com/sphinx/gameduino/

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#include "SPI.h"

#include "GD.h"

byte i;

float a = 1;

float b = 0.9;

float c = 0.4;

float d = 6;

float x = 0;

float y = 0;

float z = 0;

float xn = x;

float yn = y;

float zn = z;

float dt = 0.01;

void setpixel(byte x, byte y, byte color)

{

unsigned int addr = RAM_SPRIMG|(x & 0xf)|(y << 4)|((x & 0x30)<<8);

byte mask = 0xc0 >> ((x >> 5) & 6);

GD.wr(addr, (GD.rd(addr) & ~mask) | (color & mask));

}

void setup()

{

int i;

GD.begin();

GD.ascii();

for (i = 0; i < 256; i++) {

int x = 72 + 16 * ((i >> 4) & 15);

int y = 22 + 16 * (i & 15);

int image = i & 63;

int pal = 3-(i >> 6);

GD.sprite(i, x, y, image, 0x8 | (pal << 1), 0,0);}

GD.fill(RAM_SPRIMG, 0, 16384);

GD.wr16(PALETTE4A + 6, RGB(255,255,255));

GD.putstr(13, 1, "Ikeda chaotic attractor");

}

void loop()

{

xn = a+b*(x*cos(z)-y*sin(z));

yn = b*(x*sin(z)+y*cos(z));

zn = c-d/(1+pow(x,2)+pow(y,2));

x = x+xn*dt;

y = y+yn*dt;

z = z+zn*dt;

setpixel (128+(x/5.3), 140+(y/6),255);

}

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New-chaos

New chaotic attractor

New chaotic attractor for arduino with gameduino shield.

http://lsc.amss.ac.cn/~ljh/04LCC.pdf

http://www.arduino.cc/

http://excamera.com/sphinx/gameduino/

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Scroll-1 attractor

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#include "SPI.h"

#include "GD.h"

byte i;

float a = -10;

float b = -4;

float c = 11;

float x = 1;

float y = 1;

float z = 1;

float xn = x;

float yn = y;

float zn = z;

float dt = 0.005;

void setup()

{

GD.begin();

GD.ascii();

GD.wr16(RAM_SPRPAL + (0 * 2), 0x8000);

GD.wr16(RAM_SPRPAL + (1 * 2), RGB(255, 255, 255));

GD.fill(RAM_SPRIMG, 0, 256);

GD.wr(RAM_SPRIMG + 0x78, 1);

GD.putstr(12, 1, "New-chaos 1-scroll attractor");

}

void loop()

{

xn = -((a*b)/(a+b))*x-y*z+c;

yn = a*y+x*z;

zn = b*z+x*y;

x = x+xn*dt;

y = y+yn*dt;

z = z+zn*dt;

GD.sprite(i++, 175+(7.2*x), 130+(5.5*y), 0, 0, 0);

}

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Scroll-2 attractor

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#include "SPI.h"

#include "GD.h"

byte i;

float a = -10;

float b = -4;

float x = -1;

float y = -1;

float z = -1;

float xn = x;

float yn = y;

float zn = z;

float dt = 0.002;

void setup()

{

GD.begin();

GD.ascii();

GD.wr16(RAM_SPRPAL + (0 * 2), 0x8000);

GD.wr16(RAM_SPRPAL + (1 * 2), RGB(255, 255, 255));

GD.fill(RAM_SPRIMG, 0, 256);

GD.wr(RAM_SPRIMG + 0x78, 1);

GD.putstr(12, 1, "New-chaos 2-scroll attractor");

}

void loop()

{

xn = -((a*b)/(a+b))*x-y*z;

yn = a*y+x*z;

zn = b*z+x*y;

x = x+xn*dt;

y = y+yn*dt;

z = z+zn*dt;

GD.sprite(i++, 205+(4.5*x), 145+(3.5*y), 0, 0, 0);

}

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Sunday, March 11, 2012

Knot

Knot fractal map

Knot fractal map for arduino with gameduino shield.

http://zito.web.cern.ch/zito/aleph/chep94sl/formula.html

http://www.arduino.cc/

http://excamera.com/sphinx/gameduino/

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#include "SPI.h"

#include "GD.h"

byte i;

float x = 0.1;

float y = 0;

void setpixel(byte x, byte y, byte color)

{

unsigned int addr = RAM_SPRIMG|(x & 0xf)|(y << 4)|((x & 0x30)<<8);

byte mask = 0xc0 >> ((x >> 5) & 6);

GD.wr(addr, (GD.rd(addr) & ~mask) | (color & mask));

}

void setup()

{

int i;

GD.begin();

GD.ascii();

for (i = 0; i < 256; i++) {

int x = 72 + 16 * ((i >> 4) & 15);

int y = 22 + 16 * (i & 15);

int image = i & 63;

int pal = 3-(i >> 6);

GD.sprite(i, x, y, image, 0x8 | (pal << 1), 0,0);}

GD.fill(RAM_SPRIMG, 0, 16384);

GD.wr16(PALETTE4A + 6, RGB(255,255,255));

GD.putstr(17, 1, "Knot fractal map");

}

void loop()

{

double nx = x;

x = -y;

y = pow(nx,3)-nx-y;

setpixel (128+(85*x), 128+(85*y),255);

}

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Saturday, March 10, 2012

Basin

Basin chaotic map

Basin chaotic map for arduino with gameduino shield.

http://www.ba.infn.it/~zito/ds/basin.html

http://www.arduino.cc/

http://excamera.com/sphinx/gameduino/

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#include "SPI.h"

#include "GD.h"

byte i;

float a = 0.4;

float x = 0.1;

float y = 0;

void setpixel(byte x, byte y, byte color)

{

unsigned int addr = RAM_SPRIMG|(x & 0xf)|(y << 4)|((x & 0x30)<<8);

byte mask = 0xc0 >> ((x >> 5) & 6);

GD.wr(addr, (GD.rd(addr) & ~mask) | (color & mask));

}

void setup()

{

int i;

GD.begin();

GD.ascii();

for (i = 0; i < 256; i++) {

int x = 72 + 16 * ((i >> 4) & 15);

int y = 22 + 16 * (i & 15);

int image = i & 63;

int pal = 3-(i >> 6);

GD.sprite(i, x, y, image, 0x8 | (pal << 1), 0,0);}

GD.fill(RAM_SPRIMG, 0, 16384);

GD.wr16(PALETTE4A + 6, RGB(255,255,255));

GD.putstr(16, 1, "Basin chaotic map");

}

void loop()

{

double nx = x;

x = nx*y+a*nx-y;

y = nx+y;

setpixel (107+(79*x), 189+(93*y),255);

}

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Thursday, March 8, 2012

New-Jerk

New-Jerk chaotic circuit

New-Jerk chaotic circuit for arduino with gameduino shield.

http://sprott.physics.wisc.edu/pubs/paper352.pdf

http://www.arduino.cc/

http://excamera.com/sphinx/gameduino/

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#include "SPI.h"

#include "GD.h"

byte i;

float a = 0.00000001;

float b = 0.026;

float x = 0.1;

float y = 0.1;

float z = 0.1;

float xn = x;

float yn = y;

float zn = z;

float dt = 0.01;

void setup()

{

GD.begin();

GD.ascii();

GD.wr16(RAM_SPRPAL + (0 * 2), 0x8000);

GD.wr16(RAM_SPRPAL + (1 * 2), RGB(255, 255, 255));

GD.fill(RAM_SPRIMG, 0, 256);

GD.wr(RAM_SPRIMG + 0x78, 1);

GD.putstr(13, 1, "New-Jerk chaotic circuit");

}

void loop()

{

xn = y;

yn = z;

zn = -z-x-a*(exp(y/b)-1);

x = x+xn*dt;

y = y+yn*dt;

z = z+zn*dt;

GD.sprite(i++, 280+(155*x), 180+(155*y), 0, 0, 0);

}

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