Before N.J. Rose was a mathematician, he was an engineer. In fact, let's go back to the point in time, what year I don't know, where Rose went seeking a job at a University. Now.. you'll have to excuse me, my records and journal articles are tucked away and so I'm trying to write by memory.. Some details, I'll leave out, at risk that I may tarnish the facts with forgetfulness. If my celly were awake, I'd dig out the paperwork, but for now, just bare with me. As I was saying, Rose was seeking a job as a teacher in engineering. This period of time was such that any living thing that speaks would be admitted, due to some chance circumstance. The University was looking for a math teacher as well, and since the level of mathematics wasn't incredibly high, Rose decided upon mathematics, despite his desire for engineering. This triggered a chain of events.. It would seem that in the interim, Rose fell in love with numbers. For he earned his masters in mathematics and fell in tempo to the tune of an excellent teacher. I bring this up because of the strange happenstance at which his mathematical career began. What're the odds, right?
Fast forward... As Rose's passion for mathematics grew, he published books and articles, and even a series of mathematical calendars. Most of these were published by a "Rome Press", which seemed to exist only during the fruitful years of Rose's mathematical creativity. I have a suspicion that Rome Press may have belonged to Rose himself, and that it was an effective way to publish lower level mathematics. Whether this is the case, I can only speculate. ...if it was, it was smart. Some of the writing involved mathematical humor and ultimately reflected a genuine enjoyment for the maths. I will add, that Rose's early work, from around1980, is very rare. It's not easy to track down. Some of it is already being lost to obscurity, largely because of its availability.
Fast forward some more... 1982. Here we see a year that will cause decades of confusion. In 1982, Benoit Mandelbrot published a book showing the relationship between the Pascal's triangle modulo 2 and Sierpinski's gasket. Also, Stephen Wolfram submitted a paper "Statistical Mechanics of cellular automata". This also showed the relationship. Both Mandelbrot and Wolfram are math gods. One literally wrote THE book on fractals and the other wrote the book on cellular automata. ...there has always been a debate about whom it was that made the connection between Sierpinski's gasket and Pascal's triangle. Mandelbrot or Wolfram.
Again, if you haven't read "Watching Gold go Down the Drain", I would request that you do. You won't understand the significance of what I'm saying, otherwise. Because in one of Rose's obscure calendars, he made this connection. 1981 The Mathematical Calendar. Rose wrote a one paragraph article describing this connection and explicitly mentioning Sierpinski. It was neither Mandelbrot nor Wolfram. He even showed an illustration. I finally tracked it down. It exists, and it is being documented in an article on the history of mathematics.
Finally, I've had many discussions with mathematicians about the origins of this relationship. It's important in a historical context. It's incredibly curious to all us mathematicians who have ever done work in binomial coefficients, fractals, cellular automata, Cosmatesque flooring, and the Tower of Hanoi. ...I made a promise that I would see this through. There are a total of three citations for the 1981 Mathematical Calendar : Pascal's triangle modulo 2 and Sierpinski's tree, by N.J. Rose. This number will increase very soon.