first design in fusion360 and render with RGB lights.
Step 1: Make Hexagonal Hole in Box
use cardboard and cut into size 12cmx12 cm.
(if you need big increase size).
use ring spanner for draw hexagonal on cardboard.(see image)
Step 2: Use Arduino for Programming
Use Arduino and write program (as per image attach).
this program for blinking RGB LED in define delay (you will change delay for more example)
use ground in digital side and other 3 pin of RGB LED in 8,9,10 Digital Pin.
upload the program.
Step 3: Connect Parts
Connect RGB LED to Arduino port .
(use 110ohm resistance .)
When code run properly use power bank for power supply.
Step 4: Infinite Projection
Place 2 mirrors at 180 degree parallel.
Place hexagonal cardboard box in between two mirror.
see the magic .