Simultaneous blinking LEDs, with separate and inconsistent patterns

Question

I'm trying to run two "Blink"-esque functions simultaneously.

I've found some code elsewhere that lets me do that and modified it! Great.

However, what I am trying to do is have one LED turn on and off every 1000ms as per usual, but have the other blink in an odd pattern, like ON for 3000ms, OFF for 100ms, ON for 100ms, OFF for 200ms then loop back.

To make this happen I tried adding a random function to the code I found but I don't like how it looks. It looks like a blinking LED with interference or something, like on a radio transmitter or whatever. I'm trying to replicate an old flickering lightbulb, meaning it always has to be ON for longer than it is off, Essentially it needs to be ON/HIGH for a "longer" period of time and then interrupted by several short flashes of ON and OFF

So I'm looking for help in how I can orchestrate the 2nd LED to turn on and off in a more specific series of flickers.

Here's the code I'm using so far:

/* Blink Multiple LEDs without Delay
*
* Turns on and off several light emitting diode(LED) connected to a digital
* pin, without using the delay() function.  This means that other code
* can run at the same time without being interrupted by the LED code.
*/
int led1 = 13;                // LED connected to digital pin 13
int led2 = 12;
int value1 = LOW;                // previous value of the LED
int value2 = HIGH;                // previous value of the LED
long time1 = millis();
long time2 = millis();

long interval1 = 1000;           // interval at which to blink (milliseconds)

void setup()
{
 Serial.begin(9600);
 randomSeed(analogRead(0));
 pinMode(led1, OUTPUT);      // sets the digital pin as output
 pinMode(led2, OUTPUT);
}

void loop()
{
 unsigned long m = millis();

 if (m - time1 > interval1){
   time1 = m;

   if (value1 == LOW)
     value1 = HIGH;
   else
     value1 = LOW;

   digitalWrite(led1, value1);
 }

long interval2 = random(100,1500);

 if (m - time2 > interval2){
   time2 = m;

   if (value2 == LOW)
     value2 = HIGH;
   else
     value2 = LOW;

   digitalWrite(led2, value2);
 }

   Serial.println(interval2);
}

Answer 1

This will always take less than a second to run so you can get back to your main loop and ensure that you don't miss the 1 second on/off for the other LED:

void flicker(){
    boolean state = false;
    int r = random(20, 175);
    for(int i = 0; i < 5; i++){
        digitalWrite(led2, state);
        state = !state;
        delay(r);
        r = random(20, 175);
    }
    digitalWrite(led2, HIGH);
}

Btw. I'm replacing this toggle code:

if (value2 == LOW)
  value2 = HIGH;
else
  value2 = LOW;

digitalWrite(led2, value2);

with this:

state = !state;
digitalWrite(led2, state);

Now, call flicker() at random intervals; maybe every 15-45 seconds or whatever you find appropriate/realistic.