How can you show your self-improvement to someone you cannot meet or talk?


She [F34] broke up with me [M30] 2 months ago and moved out of our house 1 month ago due to my recurring behavior of attacking her personality when I was under external stress. Same thing happened one year ago but eventually we came back together. We were together for 3.5y in total, ready to get married. And she is the love of my life and I was hers too. But after she left she deleted me and our photos from all media, refused to call or meet in person and making it clear that she wants our communication to be minimum. After the first week I didn’t push her and I’ve been working on fixing myself with any way possible, from therapy, meditation, by studying and analyzing my behavior, reflecting on my actions, making new friends, etc. And the only thing she accepted as communication was an email-letter from my side expressing my apologies and an occasional “how are you” in a chat (again from me). We don’t have common friends and no chance to meet as we are new in this city (a very big city). I’m planning to go completely NC, hoping that she will soften and willing to at least restart some form of communication with me. But most likely she won’t because she is very determined to move on (if she hadn’t done so already). So how can I show to someone with no chance to meet or talk, my efforts on improving myself? How can I let her know of my new-self if there is no communication between us?
Well, this is something we come across fairly often in our advice sessions. I understand your fear that she might not be willing to talk to you forever. However, the first thing to realize is that forever is a very long time. Maybe she is processing things right now and so she can not or will not communicate with you. At the same time, she didn't cut off the contact completely. You can still reach her through email. With these two factors, it is a good idea to go no contact for a while. BUT: This should be announced and well prepared. You should write her a farewell letter and let her now that you are not going to contact her in the near future and that you will focus on solving the issues that made your relationship go astray. A few weeks down the road, without any communication, she might build up enough curiosity to meet with you again. There are a few other things, I would work with you on, so let me know, if you'd like to setup a session, so I can have a closer look at what is going on.
Well I still haven’t send her the apology-letter because I wanted to make sure that it’s comprehensive and focuses on the things that matter. So in it, apart from an honest apology, I explain how I came to certain understandings about myself, I show her that I understand her side and how she must have felt those moments, I thank her for our time together, and also inform her of the ways that I’m working on certain issues. I don’t ask her back, or express my feelings strongly of how much I love and miss her (I wasn’t sure if I have to). But maybe I could also include my announcement for NC in the end of the letter as you suggested...
And also even though she might built curiosity, I hardly believe she will talk to me afterwards... it’s her personality: strong, and to stick to her decisions. So that’s my biggest fear, that NC won’t work on making her softer to talk to me. Rather it will just support her to move on. Anyways, thanks for your advice. I’ll consider your services, but maybe in a few weeks time.