The code:

/*
    Clock with a 16 LED NeoPixel ring
    (C) 2016 -mat- filid brandy, brandy@linuxpinguin.de
*/

// Settings for the NeoPixel
#include <Adafruit_NeoPixel.h>
#define stripSize 16
Adafruit_NeoPixel strip = Adafruit_NeoPixel( stripSize, 6, NEO_GRB + NEO_KHZ800 );

// Time keeping
#define hs 0
#define s 1
#define m 2
#define h 3

unsigned long Diff[4];
unsigned long Max[4];
unsigned long Tick[4];
unsigned long Uhr[4];
unsigned int Pixel[4];
float Ratio[4];
bool reverse = LOW;
bool toggle = LOW;

// Colors
uint32_t colors[9];
#define black 0
#define white 1
#define red 2
#define green 3
#define blue 4
#define purple 5
#define cyan 6
#define yellow 7
#define all 8
#define light 8



void setup() {
  // Initialize the strip
  strip.begin();
  strip.show();

  Max[hs]   = 100;
  Max[s]    = 60;
  Max[m]    = 60;
  Max[h]    = 12;

  Diff[hs]  = 10;
  Diff[s]   = 1000;
  Diff[m]   = 60000;
  Diff[h]   = 3600000;

  for (int i = 0; i < 4; i++) {
    Tick[i] = 0;
    Uhr[i] = 0;
    Pixel[i] = 0;
    Ratio[i] = (float)Max[i] / (float)stripSize;
  }

  // fill in the wanted colors
  colors[black]  = strip.Color(0, 0, 0);
  colors[white]  = strip.Color(light / 4, light / 4, light / 4);
  colors[red]    = strip.Color(light, 0, 0);
  colors[green]  = strip.Color(0, light, 0);
  colors[blue]   = strip.Color(0, 0, light);
  colors[purple] = strip.Color(light, 0, light);
  colors[cyan]   = strip.Color(0, light, light);
  colors[yellow] = strip.Color(light, light, 0);
  colors[all]    = strip.Color(light * 2, light * 2, light * 2);
}

void loop() {
  // This is based on the internal Ticker
  unsigned long cTick = millis();

  // Find the trigger points in Tick
  for (int i = 0; i < 4; i++) {
    if ( (cTick - Tick[i]) >= Diff[i] ) {
      Tick[i] = cTick;
      Uhr[i] = ( ++Uhr[i] < Max[i] ) ? Uhr[i] : 0;
    }
  }

  if ( 0 == Uhr[hs] && !toggle) {
    reverse = !reverse;
    toggle = HIGH;
  }
  if ( 1 == Uhr[hs] ) {
    toggle = LOW;
  }

  // Calculate the display of
  for (int16_t p = 0; p < stripSize; p++) {
    strip.setPixelColor(p, colors[black]);
    // Find the points for the hs, s, m, h
    for (int j = 0; j < 4; j++) {
      if ( ( (float)(p) * Ratio[j] <= Uhr[j]  ) && ( Uhr[j] < (float)(p + 1) * Ratio[j] ) ) {
        Pixel[j] = stripSize - p - 1;
      }
    }
  }
  // 1/100s animation
  for (int16_t p = 0; p < stripSize; p++ ) {
    if (Pixel[hs] < p) {
      if (reverse)
        strip.setPixelColor(p, colors[white]);
      else
        strip.setPixelColor(p, colors[black]);
    } else {
      if (reverse)
        strip.setPixelColor(p, colors[black]);
      else
        strip.setPixelColor(p, colors[white]);
    }
  }

  // Paint the points
  strip.setPixelColor(Pixel[hs], colors[white]);
  strip.setPixelColor(Pixel[s], colors[green]);
  strip.setPixelColor(Pixel[m], colors[red]);
  strip.setPixelColor(Pixel[h], colors[blue]);

  // Handle overlaying points
  // double
  if ( Pixel[s] == Pixel[m] ) strip.setPixelColor(Pixel[m], colors[yellow]);
  if ( Pixel[s] == Pixel[h] ) strip.setPixelColor(Pixel[h], colors[cyan]);
  if ( Pixel[m] == Pixel[h] ) strip.setPixelColor(Pixel[h], colors[purple]);
  // triple
  if ( ( Pixel[m] == Pixel[h] ) && ( Pixel[s] == Pixel[m]) ) strip.setPixelColor(Pixel[h], colors[all]);

  // Tada!
  strip.show();
}