<human>: Could you distill the essence of the text into 1-3 sentences?

Thank you to anyone who takes the time to read this or help me!

In early June me and my gf of 3 years split up. I became distant because I was afraid of the future and had doubts. I realize this was a mistake and I have been trying to reconcile since a week before that.

I went through the usual week or two of pleading, begging, crying so on and she kept telling me she needed space and this was only making it worse. A few weeks ago I told her I understand she needs space and I respect that and I will not contact her anymore. I also told her thank you for everything and she can contact me any time and that she meant a lot to me and I had a lot of great memories. Then I removed her from snapchat and moved on and did not contact her.  

Fast forward to a few days ago she texted me and asked how I was doing and make a joke about a song she showed me a little while back. I texted back a few times but kept it short and nice and didn't seem desperate or anything. Then two days ago she "accidentally" sent me a snapchat of herself at a party. I texted her and said "was that supposed to be sent to me?" And she just said "I'm sorry." We chatted for a minute and it was very clear she was very drunk so I just kinda responded a little bit but didn't talk about anything really. At one point however she asked why I removed her on snapchat and told me she noticed I don't watch her snap stories anymore. 

The morning after that I texted her happy birthday. Since it was her birthday and told her I hope she's not too hungover. We ended up texting back and forth for about 20 or so messages and replies over like 5 hours all about good stuff and music and joking around. 

Now my question, does this mean she put out a branch for communication? I want to get back together with her and I want to take it slow? Is it okay if I text her today or tomorrow to just chat? Or should I continue to wait for her to imitate contact?

Any help would be great!!
<bot>: Ex has been texting me after she wanted no contact? Does this mean communication is open for friendly chatting/reconciliation?