Rangoli lights on an Arduino Uno

// Rangoli lights: a 16x16 panel of LEDs that draws glowing rangoli patterns,
// each one symmetric eight ways from the middle, slowly turning through the
// colors. A button moves to the next design.
//
//   panel     256 WS2812B LEDs, a 16x16 matrix, DIN <- 330 ohms <- pin 6
//   button    pin 2 -> button -> GND        (INPUT_PULLUP)
//
// At Diwali, families draw rangoli at the door: patterns of colored powder,
// rice or flower petals, often in rings of petals around a center. Most
// rangoli are symmetric, so the same shape repeats as you turn around the
// middle. That is easy to build in code: measure each LED's distance from the
// center across and down, and fold so that only the two distances matter and
// not their order. Any color worked out from them is the same in all eight
// mirror places.
//
// There are three designs: rings, a diamond lotus, and an eight-petal flower.
// Each colors an LED by a shape number plus a slowly growing offset, so the
// colors flow outward from the middle.
//
// The panel needs 768 bytes for its colors, more than a third of the Uno's
// memory. At full white 256 LEDs could draw 15 A, so the brightness is kept
// low and a real panel wants its own 5 V supply.
//
// Things to try. Press the button. Invent a fourth design in shape().

#include <Adafruit_NeoPixel.h>

const int SIZE = 16;
const int BUTTON_PIN = 2;
const int DESIGNS = 3;

Adafruit_NeoPixel panel(SIZE * SIZE, 6, NEO_GRB + NEO_KHZ800);

int design = 0;
uint16_t offset = 0;
const char *NAMES[DESIGNS] = {"rings", "diamond lotus", "eight petals"};

// A number for the LED at a, b: the two folded distances from the center,
// 1, 3, 5 ... 15 each, with a >= b.
uint16_t shape(int a, int b) {
  switch (design) {
    case 0: return (a * a + b * b) * 40;                    // rings
    case 1: return (a + b) * 600 + (a - b) * 200;           // diamond lotus
    default: return (a - b) * 900 + (a * b) % 16 * 300;     // eight petals
  }
}

void setup() {
  Serial.begin(9600);
  pinMode(BUTTON_PIN, INPUT_PULLUP);
  panel.begin();
  panel.setBrightness(40);
  Serial.println("Rangoli lights: design 0, rings");
}

void loop() {
  if (digitalRead(BUTTON_PIN) == LOW) {
    design = (design + 1) % DESIGNS;
    Serial.print("Design ");
    Serial.print(design);
    Serial.print(", ");
    Serial.println(NAMES[design]);
    while (digitalRead(BUTTON_PIN) == LOW) delay(10);
  }
  for (int y = 0; y < SIZE; y++) {
    for (int x = 0; x < SIZE; x++) {
      int dx = abs(2 * x - (SIZE - 1));
      int dy = abs(2 * y - (SIZE - 1));
      int a = dx > dy ? dx : dy;
      int b = dx > dy ? dy : dx;
      uint16_t hue = shape(a, b) - offset;
      panel.setPixelColor(y * SIZE + x, panel.ColorHSV(hue, 255, 255));
    }
  }
  panel.show();
  offset += 400;
  delay(30);
}