LED sparkler on an Arduino Uno

// Sparkler: a stick of LEDs that you light with a button. It throws gold and
// white sparks from the burning tip, and burns down toward the handle like a
// real one, then goes out.
//
//   stick     16 WS2812B LEDs, DIN <- 330 ohms <- pin 6 (LED 0 at the handle)
//   button    pin 2 -> button -> GND        (INPUT_PULLUP): light it
//
// The strip goes inside a clear or frosted tube with LED 0 at the handle end.
// The burning point starts at the far end and creeps down over BURN_MS. Above
// it the stick is spent and dark; at it, the LEDs flash at random in gold and
// white; just below it, a few glow orange where the stick is about to catch.
//
// The randomness is the whole effect. Each frame, every LED near the burning
// point gets a fresh random chance to flash, so the sparkle never repeats.
//
// A real sparkler burns at over 1000 degrees Celsius and is a common cause of
// burns on the Fourth of July. This one never gets warm, so the smallest
// people at the party can hold it.
//
// Things to try. Press the button. Make it burn for a minute with BURN_MS.
// Try a red, white and blue sparkle.

#include <Adafruit_NeoPixel.h>

const int LEDS = 16;
const int BUTTON_PIN = 2;
const unsigned long BURN_MS = 20000UL;

Adafruit_NeoPixel stick(LEDS, 6, NEO_GRB + NEO_KHZ800);

bool burning = false;
unsigned long litAt = 0;
int sparklers = 0;

void setup() {
  Serial.begin(9600);
  pinMode(BUTTON_PIN, INPUT_PULLUP);
  stick.begin();
  stick.setBrightness(200);
  stick.show();
  Serial.println("Sparkler ready: press the button to light it");
}

void loop() {
  unsigned long now = millis();
  if (!burning && digitalRead(BUTTON_PIN) == LOW) {
    burning = true;
    litAt = now;
    sparklers++;
    Serial.print("Sparkler ");
    Serial.print(sparklers);
    Serial.println(" lit");
  }
  if (!burning) return;

  unsigned long t = now - litAt;
  if (t >= BURN_MS) {
    burning = false;
    stick.clear();
    stick.show();
    Serial.println("Burned out");
    return;
  }
  // The burning point, from the tip (LEDS - 1) down to the handle.
  int tip = (LEDS - 1) - (int)((long)(LEDS - 1) * t / BURN_MS);
  stick.clear();
  for (int i = 0; i < LEDS; i++) {
    int d = tip - i;   // how far below the burning point
    if (d == 0 || (d == -1 && random(0, 2))) {
      // At the tip: flashes of white and gold.
      if (random(0, 3) == 0) stick.setPixelColor(i, 255, 255, 255);
      else stick.setPixelColor(i, 255, random(120, 200), 20);
    } else if (d > 0 && d <= 2) {
      // Just below: an orange glow, about to catch.
      int v = random(40, 120) / d;
      stick.setPixelColor(i, v, v / 3, 0);
    } else if (d < -1 && d > -5 && random(0, 6) == 0) {
      // Sparks flying off past the tip.
      stick.setPixelColor(i, 255, 220, 120);
    }
  }
  stick.show();
  delay(30);
}