Sure thing, please find answers to your questions below.
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Can you provide any more details on what these lines do?
Serial.begin(9600) initialises the serial port at 9600 bps. Reference here
Serial.print(counter) outputs the current value of the counter variable to the serial port so it can be read in the Serial Monitor Arduino window (unders Tools -> Serial Monitor.) Reference here
Serial.println(F("...")) prints the string ... (ie 3 periods) to the serial port and then ends the line (the previous print statement does not end the line, so the periods are printed right after the number. Reference here
Writing F("...") rather than simply "..." is a trick that means the "..." is stored in flash memory on the Arduino rather than being loaded into RAM - this is useful with constant strings that don't change, as it saves some RAM, but it's not strictly necessary. It is documented under the "Print" documentation linked above.
[*] In your changelog, you mentioned integrated timer management. Can you explain what this means please?
In the original DMD library example sketches, you'll see a lot of code involved with using the "Timer1" feature of the Arduino microcontroller to automatically refresh the display at the correct interval. In DMD2 all of this timer code is integrated in the library for simplicity, you don't need to include it in each sketch you write.
[*] Does the brightness default to maximum? Or some other value? Also, can I confirm that 255 is the maximum? What is the minimum? (i.e. 0 or 1).
It defaults to maximum, which is 255. 0 is the minimum, but the display will be off in this case. The display may not be visible at brightness level 1 or 2.
[*] What do dmd.fillScreen() and dmd.clearScreen() do?
The former turns on every LED, the latter turns off every LED.
[*] Does this library support daisy-chaining? Does it work the same as for the original DMD library? (i.e. you refer to it all as one big board with more coordinate points).[/list]
Yes, absolutely. The "GameOfLife" example probably has the best example code for this at the moment:
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// How many displays do you have?
const int WIDTH = 2;
const int HEIGHT = 1;
Allowing you to create a large integrated display.
Apologies for the still-slow progress on the DMD2 beta, but I'll hopefully get some more time to finish it off soon.