Displaying Ulam Spirals with Arduino Yun and 128x160 Display

I just set up a small 128x160 LCD display with an Arduino Yun running full animations of the Ulam Spiral. 

Here's the adafruit tutorial I used to get going: http://www.adafruit.com/products/358

Notes: the redraw rate is pretty slow, around 1 frame per 3 seconds or so. Definitely not as fast as the LED panel I wired up. It's still very interesting to watch the spirals develop like this and much faster then Flash. The other cool thing about this build is the Yun, which I have connected to a wireless network. It's very easy to update the board remotely. 

Here's the code from my sketch: 

//spiral algo written by arlo emerson arloemerson@gmail.com

//adapted from the ulam spiral aglorithm

//2014

//http://ulamspiral.blogspot.com/

#define PI 3.1415926535897932384626433832795

#define sclk 4

#define mosi 5

#define cs   6

#define dc   7

#define rst  8 

#include    // Core graphics library

#include // Hardware-specific library

#include

#if defined(__SAM3X8E__)

#undef __FlashStringHelper::F(string_literal)

#define F(string_literal) string_literal

#endif

Adafruit_ST7735 tft = Adafruit_ST7735(cs, dc, mosi, sclk, rst);

#define Neutral 0

#define Press 1

#define Up 2

#define Down 3

#define Right 4

#define Left 5

float _piCounter = .005;

int _globalCounter = 2;

void setup(void) {

  Serial.begin(9600);

  tft.initR(INITR_BLACKTAB); 

  uint16_t time = millis();

  tft.fillScreen(ST7735_BLACK);

  time = millis() - time;

  tft.drawPixel(tft.width() / 2, tft.height() / 2, ST7735_GREEN);

  printWelcomeText();

  initSpiral();

}

void loop()

{

  initSpiral();

  _piCounter += .001;

  delay(200);

  _globalCounter += 1;

  if (_globalCounter == 10)

  {

    printWelcomeText();

    _globalCounter = 0;

  }

}

void initSpiral()

{

  int posX = tft.width() / 2;

  int posY = tft.height() / 2;

  int numberCounter = 1;

  int _spacer = 1;

  int legLength = 0;

  //establish the first dot

  tft.drawPixel(posX, posY, ST7735_WHITE);

  for (int i = 1; i < 60; i++)

  {

    for (int k = 0; k <= legLength; k++)

    {

      numberCounter += 1;

      posX += _spacer;

      testNumber(numberCounter, posX, posY);

    }

    for (int k = 0; k <= legLength; k++)

    {

      numberCounter += 1;

      posY -= _spacer;

      testNumber(numberCounter, posX, posY);

    }

    legLength += 1;

    for (int k = 0; k <= legLength; k++)

    {

      numberCounter += 1;

      posX -= _spacer;

      testNumber(numberCounter, posX, posY);

    }

    for (int k = 0; k <= legLength; k++)

    {

      numberCounter += 1;

      posY += _spacer;

      testNumber(numberCounter, posX, posY);

    }

    legLength += 1;

  }

}

void testNumber(int pNumber, int pX, int pY)

{

  //int tmpMultiplier = _piCounter * 1.1;

  //if (round(sqrt(pow(pNumber,2))*(1.6180339887*PI)/2)%2==0)

  //if (round(  pow(sqrt(pNumber)/PI, tmpGradient) )%2==0)

  //Serial.println(_piCounter);

  //if (round( sqrt( pow(pNumber, 2 ))*_piCounter * PI) % 2 == 0)

  //if (round(sqrt(pow(pNumber,2))*((.9 * _piCounter) *PI)/2)%2==0)

  if (  round( (pX*pY)* pow(sqrt(pNumber)/PI, 1.23456789)*_piCounter )%3==0)

  {

    //    matrix.drawPixel(pX, pY, matrix.Color333(_bigNumber.charAt(pX), _bigNumber.charAt(pY), _bigNumber.charAt(_globalCounter)));

    tft.drawPixel(pX, pY, ST7735_WHITE);

  }

  else

  {

    tft.drawPixel(pX, pY, ST7735_RED);

  }

}

void printWelcomeText()

{

  tft.setCursor(0, 0);

  tft.fillScreen(ST7735_BLACK);

  tft.setTextColor(ST7735_YELLOW);

  tft.setTextSize(2);

  tft.println("Ulam");

  tft.setTextColor(ST7735_WHITE);

  tft.println("Spirals");

  tft.setTextColor(ST7735_RED);

  tft.println("Forever");

  delay(3000);

  tft.fillScreen(ST7735_BLACK);

}

Ulam Spirals Using Arduino and LED Displays

Here's an animated gif of my Arduino-powered 32x16 LED screen. I wired this up using the Adafruit tutorial at https://learn.adafruit.com/32x16-32x32-rgb-led-matrix/wiring-the-16x32-matrix

The code to generate the spiral. Note this is unoptimized. You can probably do it better. The basic nugget to get the spiral is this line: round( sqrt( pow(pNumber, 2 ))*_piCounter*PI)%2==0).

void loop()

{

   initSpiral();

  _piCounter += .001;

  delay(200);

  _globalCounter += 1;

}

void initSpiral()

{

  int posX = 15;

  int posY = 7;

  int numberCounter = 1;

  int _spacer = 1;

  int legLength = 0;

  //establish the first dot

  //matrix.drawPixel(x, y, matrix.Color333(r, g, b));

  matrix.drawPixel(posX, posY, matrix.Color333(3, 4, 5));

  for (int i=1;i<17 font="" i="">

  {

    for (int k=0;k<=legLength;k++)

    {

      numberCounter += 1;

      posX += _spacer;

      testNumber(numberCounter, posX, posY);

    }

    for (int k=0;k<=legLength;k++)

    {

      numberCounter += 1;

      posY -= _spacer;

      testNumber(numberCounter, posX, posY);

    }    

    legLength += 1;

    for (int k=0;k<=legLength;k++)

    {

      numberCounter += 1;

      posX -= _spacer;

      testNumber(numberCounter, posX, posY);

    }

    for (int k=0;k<=legLength;k++)

    {

      numberCounter += 1;

      posY += _spacer;

      testNumber(numberCounter, posX, posY);

    }

    legLength += 1;

  }

}

String _bigNumber = "01234567012345670123456701234567012345670123456701234567012345670123456701234567012345670123456701234567012345670123456701234567";

void testNumber(int pNumber, int pX, int pY)

{

  if (round( sqrt( pow(pNumber, 2 ))*_piCounter*PI)%2==0)

  {

    matrix.drawPixel(pX, pY, matrix.Color333(_bigNumber.charAt(pX), _bigNumber.charAt(pY), _bigNumber.charAt(_globalCounter)));

  }

  else

  {

    matrix.drawPixel(pX, pY, matrix.Color333(3, 0, 2));

  }

}

Interesting note: these 32x16 panels are so incredibly bright they are painful to look at. So I'm using two sheets of paper to stop down the light, which also has a nice diffusion effect.

Gaussian White Noise Wave Functions

Various examples of ulam spirals using a continuous tube to plot the points in conjunction with a white noise wave function to plot the z-coordinate. Generator written in Python using the VPython library.






Some other shapes using the gaussian white noise to determine dimensions of plot objects.

Spiral Video Series

Using smplayer/mencoder to convert PNG output to video. Formula and other control info is automatically inserted into the beginning of the video. This set is using a 2x2 pixel plotted out using the Ulam spiral "RULD" method. Pixel is black or red if the pixel number (pInt) passes the following test (e.g.): if round(((pInt)*pi)*pow(sqrt(pInt)/pi+(_multiplier/9), (1.2)) )%2==0: Iterating the value of _multiplier (or any other variable), we generate a new PNG file when the _range value is met. Stitching these images together into a video reveals motion within the overall pattern. For example, incrementing _multiplier very slightly for each image creates less disruption from one image to the next. Frame rate varies, generally within 2 to 15 FPS. Too bad blogger is overcompressing these, they are quite nice before they hit the FLV codec. C'est la vie.




Here's one of the first videos I cobbled together, a very quick prototype...

Random Grids

Detail:


I was bored today so I modified the base routine to select a cardinal direction randomly. These images are all built pulling from a list of 1,296 possible 2x2 pixel images. The original image is...

Marilyn Hex

Jaco Pastorius, Meet Stanislaw Ulam

These are all using a very simple test for n, round( pow(pInt,sqrt(1))/pi )%2==0

Enter Jeff Buckley

...and Jimi