My ex is likes desperate for my attention. Why?

So more than 3 months ago, my ex-girlfriend broke it off with me saying she needed space. I agreed and didn't bother to fight for her back. Whatever. Two weeks after she called it off, she started to hang around with someone who she didn't like. (she told me she didn't like him when she was with me). I know she's trying to get a reaction out of me so whatever. I'm ignoring it.

I see her a lot as we do go to the same gym. The other night, I was having a conversation with a female friend (She knows of me and my ex). My ex and her friend couldn't stop staring at us. Later on, my friend decided to take a photo of her surroundings. Which oddly enough caught my ex and her friend staring at her taking the photo. I think they assume something is going on between us. Like, why would she be jealous? we're not even flirting. When I talk to the girl, i just walk up to her and say hi. That's about it. My ex and that friend used to be acquaintances, now my ex fully ignores her. I think that's messed up.

According to my friend, my ex's back would be facing us but her eyes would be locked on us. Observing us. Then the following day, my ex seems to try and grab my attention again playing these games.

Why behave like this?
My ex is likes desperate for my attention. Why?
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