FINAL THOUGHTS

If someone asks me before this project, "What is a Pascal's Triangle?" I would have quickly answered that it is an arithmetic triangle composed of the coefficients of the polynomial (1+x)ⁿ, just like a grade 6 student. But if you ask me now, I can finally answer you like a university student. Pascal's Triangle is not only an arithmetic triangle, it is also a base of many different patterns. Sierpinski's Triangle is one of the most famous patterns originated from the Pascal's Triangle when you colour the odd coefficients black and the even coefficients white. And then from Sierpinski's Triangle, we relate to the important concepts of self-similarity in patterns. Therefore leading us to the three approaches in capturing the patterns of Pascal's triangle: number theory, cellular automata, or by iterated function system.