Let's contrast again the high temperature behavior with that near the critical temperature. This time, focus on the patterns in the left hand display. First, run at the preset temperature of 100 J. You may wish to stop to look at the static rather than the dynamic pattern. Then change the temperature to 2.8 J and repeat. Formally the qualitative change you have seen is quantified in terms of a correlation length. The critical temperature in an infinite system is characterized by a divergence of the correlation length.
While the program is running, grab the temperature slider handle with the cursor and watch the pattern change as you slowly change the temperature. It's tempting to try to find the transition temperature this way: you will find it very frustrating! Why?