After looking for examples on Google, I had the idea to make like a Binary counter with LEDs. I am going to use an NE555 and CD4020. It's bacically binary logic and clock generation using classic CMOS and Timer integrated circuits. The NE555 is configured in astable mode and act as the system's heartbeat. The CD2040 receive the clock pulses and each stage of the counter divides the frequency of the previous one by two. By adding LEDs, we can create a visual representation of binary increments.

Visual Feedback : 12 LEDs displaying the counting sequence from $2^0$ to $2^{13}$.
Manual Reset : A dedicated switch to clear the counter and restart from 00000000000000.

Following the datasheets, these are the specs :

Supply Voltage : 5V to 12V DC. We will use 9V
Logic Level : CMOS.
Architecture : Asynchronous (Ripple) Counter.

I changed the instructable connections by having just 12 LEDs to represent the 14 stages the CD4020 has. I also added a switch between R and +12V to have the possibility to reset the circuit anytime ! In the screenshot, the circuit has a 56nF capacitor (really small) to accelerate the process as Falstad is not using real time simulation.

For the real circuit, I'll be using 4.7uF for the whole thing to last aprox 10 minutes. And to easily calibrate everything, I'll also be using +9V instead of +12V

I used the Falstad's diagram I previously showed to make this schematic.

First step of the PCB, with all components correctly arranged and a GND pour around the LEDs

Each LED represents a specific power of 2 in the binary system. To find the current decimal value of the counter, simply add up the values of all the LEDs that are currently turned on.
It goes from 1 to 8 because the 2nd and 3rd stage of the CD4020 have no output to show on a LED. However, the time is still respected as the stage are well here.