LED Matrix pattern

So I built a standard jumper Row + Column LED matrix (using individual LEDs) Its currently 2x5. What I want to understand is how, if I wanted to, could I make patterns in there, without using a really bulky and ugly "counting" system.

I see words in there, but not much meaning.

Jesus, I must learn to multi-task better while typing. Essentially this is what I have:

1:* * 2:* * 3:* * 4:* * 5:* * a b

with each * being 1 LED. I want to make a pattern, flash through it. Right now I have an ugly if else statement just cycling the lights through it, but I want something less bulky and more dynamic.

Post what you have. Having said that, a for loop and an array of data describing the pattern are likely going to be a working answer

edit: spelling

int ROW = 9;
int COL = 4;
int count = 1;


void setup() {
  pinMode(4, OUTPUT);
  pinMode(5, OUTPUT);
  pinMode(9, OUTPUT);
  pinMode(10, OUTPUT);
  pinMode(11, OUTPUT);
  pinMode(12, OUTPUT);
  Serial.begin(300);
}

void loop() {
 Serial.print("Column: ");
 Serial.print(COL);
  Serial.print(10, BYTE);
 Serial.print("Row: ");
 Serial.print(ROW);
  Serial.print(10, BYTE);
 Serial.print("Count: ");
 Serial.print(count);
   Serial.print(10, BYTE);
  
    if (COL == 4 && count == 1)
  {
 digitalWrite(4, LOW);
 digitalWrite(5, HIGH);
 COL = 5;
  }
  
  
 else 
  {
    if (count == 1){
 digitalWrite(5, LOW);
 digitalWrite(4, HIGH);
 COL = 4;
    }
  }

  
  count = 0;
 

 
 if (ROW < 13)
 {
   digitalWrite(ROW, HIGH);
   digitalWrite(ROW-1, LOW);
   delay(50);
   ROW = ROW+1;
 }
 
 
 if (ROW == 13)
 {
   digitalWrite(ROW, HIGH);
   digitalWrite(ROW-1, LOW);
   delay(100);
     count = 1;
     ROW = 9; 
 }
 
}