Yes, I use the UNO for my OLED power supply, but I use 5V not 3.3V. I also try use 3.3V on UNO as you said, but there is no words appeared.
I try to use 2X AA as you said for external source, the OLED screen flash once(font is white and bright) and then disappear.
I use another power bank(0.5A) and plug a USB FTDI(3.3V and GND pins to OLED) for OLED power supply, the screen is fine. But, if I press reset button on UNO
at this time, the screen will be become no words on OLED.
Does it mean that OLED needs to reset with UNO at the same time? All my testings above are power on UNO first and then power on OLED, if there are words appear, I will press reset button once on UNO.
OLEDs require some power. OLEDs of that size can easily draw 100mA and more (up to 400mA). The question is, how do you power your OLED. If the OLED is powered by the 3.3V output of the Arduino, then the power could break down after some (short) time. As far as i remember, the Arduino 3.3V can only provide 50mA. Maybe enough as long as the OLED is black, but insufficient as soon as something is displayed. I suggest to power the OLED by some external source (I often use 2x AA in my projects).
Another option might be, that the init sequence for the OLED is incorrect. The init sequence in u8glib has been written for the NHD OLED, so it might be different for your OLED. But from your description, i assume, that your power source can not provide enough current.