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rqt_plot does autoscaling of the data, so the plot may look different from one run to the next if the limits are different, and ROS does not guarantee delivery of every message, so rqt_plot may miss a few messages at startup. This is probably normal.

On the other hand, if sometimes it displays a square wave, and other times it displays a smiley face, there's probably something wrong. It would really help if you described HOW the plots are different, and maybe included screenshots the show how the plots are different.