Capacitor charging voltage showing ripples on scope. Origin?
Q: Could someone tell me the origin of the ripples?


The most likely situation is is conducted emissions from either the USB, PC or Arduino. The Arduino has 10mΩ's between it and the PC on the USB's cable ground and some inductance. If there is a shifting load (likely from the Arduino or USB packets being sent repetitively) then it causes a shift in current on the USB ground. The USB ground is not a superconductor, it is a resistor, and anytime you have a resistor with shifting current the voltage also changes. This would cause the entire ground of the system to change. It's not uncommon with digital systems to see shifts of a few mV.

The most interesting thing is that 'heartbeat' is not the yellow trace, this indicates that it's most likely a current local to the 555 timer through ground.  

The scope it also likely contributing to the situation by creating a ground loop (unless your using a differential probe), as the ground of the scope is most likely connected to AC mains, and so is the ground in the PC.