Count me among the skeptics. I must admit when I read the title of your article, my first thought was what a bunch of preposterous gibberish. But in all fairness, I read it carefully to see why you had come to this conclusion. There is a certain logic in what you have presented. Unlike many, I have long been fascinated by fractals. The best example (with which most would be familiar) is the so-called butterfly effect. A butterfly flapping its wings in China today creates a hurricane in the Caribbean next week. The whole premise of fractals being small changes repeated so many times that they create large unexpected effects, raises at least the question as to whether there may be some truth in what you are proposing.
In spite of the fact that you caused me to stop and think, I suspect there are better explanations of some of the periodic symptoms you have personally experienced on a cyclical basis. The primary cause of PMS and PMDD (a more debilitating form of PMS) is due to fluctuations in estrogen levels during a woman’s menstrual cycle. Estrogen levels rise and fall twice. Levels rise during the mid-follicular phase and then drop precipitously after ovulation. This is followed by a secondary rise in estrogen levels during the mid-luteal phase with a decrease at the end of the menstrual cycle. Physical symptoms are closely tied to these changing hormone levels.
Having said this, it has been observed that severity of PMS is sometimes related to undiagnosed depression, though depression in and of itself is not the primary cause. It also has been speculated that fluctuation of serotonin levels in the brain (thought to be crucial to mood) may trigger PMS if present in insufficient amounts and also lead to fatigue, food cravings and sleep problems. Thus, while it is clear that PMS is primarily related to hormonal fluctuations during the ovulation cycle, there may be secondary things which also affect the presence and severity of symptoms. Being generous and giving you the benefit of the doubt, some of what you propose may have some basis in fact, but I still have my doubts looking at the evidence as a whole.
Trans women do not have menstrual cycles and therefore do not go though monthly hormonal level fluctuations. There are some variations in the level of estrogen available in the blood of trans women depending upon when the last dose was administered, but these do not equate to long monthly cycles, rather hourly or perhaps daily variations over a period of several days. The timing of the kind of symptoms you are experiencing are unrelated to the fluctuations related to dosage and biological half life which are much shorter than monthly. To suggest that it may be related to the cumulative, fractal effects of frequent dosing is a bit of a stretch in my opinion.
What is more likely is a sympathetic kind of symptomology. Knowing that many women experience PMS and because of your identity as, and friendship with, women, I suspect what is going on is that mentally you have subconsciously convinced yourself to experience the same kind of symptoms that they do on the same kind of monthly schedule. This is similar to the placebo effect that is seen in medicine, which is the reason that new drugs are tested in double blind studies. One group is given the new agent and a control group are given a harmless sugar pill. This helps differentiate between authentic pharmacological actions and those which are purely subjective. This effect is well-known and well established. It appears to me that you are undergoing something similar with your monthly cycle.
In any case, you propose an interesting theory which is not completely without merit. I tend to think that it is not based in reality, but one never knows. At least it forced the reader to think about the subject more carefully