There are many bad schematics and pictures online, and these pictures are really bad.
Do not try to make that. You may damage the Arduino board and the transistor.
- Even the picture of the BC548 is wrong. The BC548 is always
called "BC548" and never "BC-548".
- The BC548 is not a good choice to drive a motor. It can only
do 100 mA continuous.
- The DC barrel socket has plus and minus wrong connected.
The 12V plus is connected to the Arduino GND.
That is not okay.
- The transistor in the first picture is probably a
transistor with the pins in BCE order.
- A resistor is missing to the base of the transisor.
- Because of the missing resistor, the Arduino board
can be damaged.
When the breadboard has a bad connection to GND,
the 12V can go to pin 9 of the Arduino board.
@Dorian, there are no mystical higher alien intelligent thoughts for that schematic. It is obvious a wrong circuit that is meant to drive a motor with PWM using a transistor.
And last but not least:
There are a few different types of computer fans. Some have a capacitor inside and some will only accept a PWM signal to a PWM input.
Are you sure that your fan is able to accept PWM for the 12V power?