Easy project, hardest part is to get everything tidily inside.

Doesn't show clearly in the video, but the breathing is very linear and it glows nicely out of the windows too.
https://www.youtube.com/watch?v=DMVMIuP2tLc

You can mostly customize everything, because in example it's not necessary to have such a huge battery pack. But atleast it can last a month with two AAs :D

Things you need:

• 5mm led (or 3mm if you print in under 130% scale. It was a close fit with some black paper around it to block light from shining into the roof (poor filament choice))
  https://www.banggood.com/50Pcs-5mm-Round-Red-Green-Blue-Yellow-White-Water-Clear-Diffused-LED-Light-Diode-Lamp-p-1077217.html?p=UB260317544198201712

• AtTiny45/85: https://www.ebay.com/itm/1PCS-MCU-IC-ATMEL-DIP-8-ATTINY45-20PU-ATTINY45-TINY45-20U-TINY45-20U/401500435379?hash=item5d7b4a73b3:g:LLoAAOSw~CFY5gv0

• Arduino or something else to program the ATtiny

• 2x AA battery pack w/ switch https://www.ebay.com/itm/2-x-AA-3V-Battery-Holder-Connector-Storage-Case-Box-ON-OFF-Switch-With-Lead-Wire/112855488640?hash=item1a46b61880:g:6GIAAOSw01dZnWnZ

You can easily fit arduino nano in the police box, but I decided to use 8pin ATtiny45 because it can operate with just voltage of 1.8V. You still cannot use rechargeable cells or the led will be too dim :/

I firstly followed an out dated tutorial for programming the ATtiny so BE CAREFUL you might be wasting your time. None the less this is the tutorial that worked like a charm: http://highlowtech.org/?p=1695
If you cannot get it to work, explain your problem in the comments :)

After i got the test code working i took the example fade sketch and changed the settings until I was satisfied and uploaded it. Then wired it more permanently and I also added an extra button to bypass the chip so the tardis could be used as a static night light also.
It took like an hour to get everything inside the tardis, but hot glue makes everything perfect.

Ps. Here's the code if you're lazy:

int led = 0;
int brightness = 0;
int fadeAmount = 2;
void loop () {
analogWrite(led, brightness);
brightness = brightness + fadeAmount;
if (brightness == 0 || brightness == 180) {
fadeAmount = -fadeAmount ;}
delay(38);}