I have always rocked back and forth but I do less obvious stuff if there is anyone around. It is so ingrained into me now that I didnt really think I did it until I was reading about it and realised I was rocking while reading - and had been for some time. I was also speaking my thoughts aloud for good autistic measure. At school the more noticeable stim was rocking my head from side to side, often as I talked to/at people. Kids made my life a misery for doing this so I gradually stopped myself doing it most of the time now - not easy since I never realise when I am doing it unless I check myself. I still notice I do it a little when I see myself in a video sometimes.
I agree that it centres and soothes as well as helping with anxiety a little. If I am concentrating on something it can help me focus also.
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AQ46, EQ9, FQ20, SQ50
RAADS-R: 181 (Language: 9, Social: 97, Sensory/Motor: 37, Interests: 36)
Aspie Quiz: AS129, NT80
Alexithymia: 137