This is the first LED matrix iv'e made since i got into Arduino. So i took my own approach to assemble it and to get it working. I did not look up any tutorials and i used stuff i had laying around to built it. It actually took me 3 months to completely understand how it works :). 

I used:

• 1 old prototype board i had laying around.
• 1 Arduino pro mini.
• 16 white LED's i got from a chinese headlamp.
• 4 200ohm resistors (still can't remember why but i can't change them).
• 1 On/off switch.
• 1 Reset button. 

Then i did the following: 

• Made 8 LED rows.

• Connected the LED rows with the digital pins of the Arduino pro mini. 

• Made a variable for the delay. 

int delayAmount = 1; 

• Made a variables for each of the rows. 

int ledPinLow1 = 10;
int ledPinLow2 = 11;
int ledPinLow3 = 12;
int ledPinLow4 = 13;

int ledPinHigh1 = 6;
int ledPinHigh2 = 7;
int ledPinHigh3 = 8;
int ledPinHigh4 = 9;

• Made an imaginary table from 1 to 16 where each LED represents a number in the 4X4 matrix. 

• Made a function for each one of them open and assigned them one table number. 

void ledOne() {
  digitalWrite(ledPinLow4, HIGH);
  digitalWrite(ledPinHigh2, HIGH);
  digitalWrite(ledPinHigh3, HIGH);
  digitalWrite(ledPinHigh4, HIGH);
}

void ledTwo() {
  digitalWrite(ledPinLow4, HIGH);
  digitalWrite(ledPinHigh1, HIGH);
  digitalWrite(ledPinHigh3, HIGH);
  digitalWrite(ledPinHigh4, HIGH);
}

void ledThree() {
  digitalWrite(ledPinLow4, HIGH);
  digitalWrite(ledPinHigh1, HIGH);
  digitalWrite(ledPinHigh2, HIGH);
  digitalWrite(ledPinHigh4, HIGH);
}

void ledFour() {
  digitalWrite(ledPinLow4, HIGH);
  digitalWrite(ledPinHigh1, HIGH);
  digitalWrite(ledPinHigh2, HIGH);
  digitalWrite(ledPinHigh3, HIGH);
}

void ledFive() {
  digitalWrite(ledPinLow3, HIGH);
  digitalWrite(ledPinHigh2, HIGH);
  digitalWrite(ledPinHigh3, HIGH);
  digitalWrite(ledPinHigh4, HIGH);
}

void ledSix() {
  digitalWrite(ledPinLow3, HIGH);
  digitalWrite(ledPinHigh1, HIGH);
  digitalWrite(ledPinHigh3, HIGH);
  digitalWrite(ledPinHigh4, HIGH);
}

void ledSeven() {
  digitalWrite(ledPinLow3, HIGH);
  digitalWrite(ledPinHigh1, HIGH);
  digitalWrite(ledPinHigh2, HIGH);
  digitalWrite(ledPinHigh4, HIGH);
}

void ledEight() {
  digitalWrite(ledPinLow3, HIGH);
  digitalWrite(ledPinHigh1, HIGH);
  digitalWrite(ledPinHigh2, HIGH);
  digitalWrite(ledPinHigh3, HIGH);
}

void ledNine() {
  digitalWrite(ledPinLow2, HIGH);
  digitalWrite(ledPinHigh2, HIGH);
  digitalWrite(ledPinHigh3, HIGH);
  digitalWrite(ledPinHigh4, HIGH);
}

void ledTen() {
  digitalWrite(ledPinLow2, HIGH);
  digitalWrite(ledPinHigh1, HIGH);
  digitalWrite(ledPinHigh3, HIGH);
  digitalWrite(ledPinHigh4, HIGH);
}

void ledEleven() {
  digitalWrite(ledPinLow2, HIGH);
  digitalWrite(ledPinHigh1, HIGH);
  digitalWrite(ledPinHigh2, HIGH);
  digitalWrite(ledPinHigh4, HIGH);
}

void ledTwelve() {
  digitalWrite(ledPinLow2, HIGH);
  digitalWrite(ledPinHigh1, HIGH);
  digitalWrite(ledPinHigh2, HIGH);
  digitalWrite(ledPinHigh3, HIGH);
}

void ledThirteen() {
  digitalWrite(ledPinLow1, HIGH);
  digitalWrite(ledPinHigh2, HIGH);
  digitalWrite(ledPinHigh3, HIGH);
  digitalWrite(ledPinHigh4, HIGH);
}

void ledFourteen() {
  digitalWrite(ledPinLow1, HIGH);
  digitalWrite(ledPinHigh1, HIGH);
  digitalWrite(ledPinHigh3, HIGH);
  digitalWrite(ledPinHigh4, HIGH);
}

void ledFifteen() {
  digitalWrite(ledPinLow1, HIGH);
  digitalWrite(ledPinHigh1, HIGH);
  digitalWrite(ledPinHigh2, HIGH);
  digitalWrite(ledPinHigh4, HIGH);
}

void ledSixteen() {
  digitalWrite(ledPinLow1, HIGH);
  digitalWrite(ledPinHigh1, HIGH);
  digitalWrite(ledPinHigh2, HIGH);
  digitalWrite(ledPinHigh3, HIGH);
} 

• Made a function for all of them closed. 

void ledClose() {
  digitalWrite(ledPinLow1, LOW);
  digitalWrite(ledPinLow2, LOW);
  digitalWrite(ledPinLow3, LOW);
  digitalWrite(ledPinLow4, LOW);
  digitalWrite(ledPinHigh1, LOW);
 digitalWrite(ledPinHigh2,...