• ← Nest
• → NestWhile

NestList

WMA link

NestList[f, expr, n]

starting with expr, iteratively applies f n times and returns a list of all intermediate results.

• • NestList[f, x, 3]

• • NestList[2 # &, 1, 8]

Chaos game rendition of the Sierpinski triangle:

• • vertices = {{0,0}, {1,0}, {.5, .5 Sqrt[3]}};

• • points = NestList[.5(vertices[[ RandomInteger[{1,3}] ]] + #) &, {0.,0.}, 500];

• • Graphics[Point[points], ImageSize->Small]