Can you make a waveform asymmetrical with the 555 timer?
555 it is a legend bi or monostable oscillator with a quite sufficient accuracy (at around 1%~0,1%) and with stable operation. This general characteristics plus the low price mace this circuit to survive for decades. All this years of using, lot of “tricks” developed by the people they doing what they want it to.

But it is not a function generator and has it's limitations.

Maximum operating frequency is 300kHz - 500kHz

Duty cycle adjustment is not between 0% and 100% but it is within reasonable range (around 5% or higher and 95%). This can improve if you are use a 556: One to set frequency and the second as a one shot of variable width (duty cycle). But the same you can do with two opamp, at the same cost of 555!



The output of the 555 can be 0.5v to 1.5v above ground, so a trick is how to get a bipahse signal is to use a capacitor network and some load.



I can reccomend a good function generator that can build around an 8038 chip