How can the pattern (01001100011100001111...) be visually represented in Java (Or Elsewhere)?

I will start by describing how I discovered this pattern myself, but this information isn't directly relevant to understanding the pattern itself. If you prefer to skip the next paragraph that perfectly fine. So I was meditating under an apple tree in an orchard which is practically on my campus. There were many flies around. At first when they were flying around my nose I would shew them away, but eventually I decided to let them be. Why? Because I thought it would be a zen thing to do. At first the fly seemed to be crawling around my nasal area randomly, but then a pattern emerged. I noticed the fly went around my left nostril once, right once, left twice, right twice. At this point I decided to count these as 0's and 1's. Around this time the fly went in and out of the very edge of my left nostril three times and then the right three times. What message does the fly have for me? 010011000111... Allow that I chose to read these binary numbers from left to right in this regard. In thinking about this pattern I decided there were two main ways to interpret it. The first involves looking at the whole thing as one large number. The first 0 shows a 0 in the 1 place. The 1 place has a 1. Next is a 0 in the 4 and 8 place. And then a 1 in the 16 and 32 place. The second method involves looking at the numbers as a sequence. The first number is 01 in Binary or 2 in human. And then 0011 or 12. Next is 000111 or 56. On a graph every integer starting from makes up the X values. Using the last example allow 000111 and 56 to be Y. A third variable is Z. For any given X, Z=(The Y value of X+1)-(The current Y value associate with X). This allows one to track the rate of change. Just to see if there are more variables that may have something interesting to say, A=Z/X. B=Z/Y. C=X/Y. D=A/B. E=B/C. F=C/D. G=D/E. Etc. Attached are some images of some work I did with this pattern on a Whiteboard. You might be saying to your self, "but what exactly do you want from me?" Well I would like to see if some of these variables have interesting relationships when represented visually. I will add that the only reason I request Java is because I am most familiar with it. Does another language exist that might be more appropriate? Yes.enter image description here The first version or interpretation with a table of the data. The right side of the board. It shows the second interpretation's data and a chart.