Forum Discussion
Create a 'Triforce' array (Sierpiński Triangle) with a formula
I've been studying 'pyramid' arrays lately and with a new Zelda title out, I was inspired to generate a left-justified 'Triforce' array with a formula.
Sierpiński triangle - Wikipedia
I took the approach of identifying and keeping the odd binomial coefficients and discarding evens.
Sierpiński
=LAMBDA(r,c,LET(n, INT(COMBIN(r - 1, c - 1)), IF(AND(r = 1, c = 1), 1, IF(c <= r, IF(ISODD(n), 1, ""), ""))))
Triforce
=LAMBDA(dim,MAKEARRAY(dim, dim, Sierpiński))
I'm interested in any other creative approaches to creating this array!
6 Replies
- ok this ISODD() (pun intended). there are a couple of errors in your output and I don't think due to the formula. In particular on cell(26,11) the calculation is COMBIN(25,10) which = 3268760 and the result of ISODD is TRUE. This is the classic roundoff / representation inside of excel causing issues so you need to add INT() around that COMBIN (or around the N)
On another note I complicated the formula a bit for aesthetic improvements:
=MAKEARRAY(K2,K2,LAMBDA(r,c, IF(AND(r = 1, c = 1), "\", IF(c = r,"\",IF(c<r, IF(ISODD(INT(COMBIN(r - 1, c - 1)) ), IF(ISODD(INT(COMBIN(r - 2, c-1 )*COMBIN(r-1, c ))),"X","\"), ""), "")))))or using characters I found in the Cambria Math font I could get:
The left justified one is straightforward and maybe too easy! This one below (Image) would take some work to add spaces where needed for the sake of appearance in Excel:
11 1
1 1 1
