Replicating triangles, using the 'calc' tikz library.

Edit and compile if you like:
% Author : Hugues Vermeiren% Replicating triangles\documentclass[border=10pt]{standalone}\usepackage{tikz}\usetikzlibrary{calc}\newcommand{\construct}[3]{\foreach \n in {1,...,\nmax} {\coordinate (#3) at ($(#2)!0.5!(#3)$);\coordinate (D) at (#2);\coordinate (#2) at ($(#2)!1.0!{-60}:(#3)$);\coordinate (#1) at (D);\fill [blue!10] (#1) -- (#2) -- (#3) -- cycle;\draw (#3) -- (#2) -- (#1);}}\newcommand{\basetriangle}{% equilateral triangle with side 1\def\h{0.866025}% sqrt(3)/2\coordinate (X) at (-1/2,{-1/3*\h});\coordinate (Y) at (1/2,{-1/3*\h});\coordinate (Z) at (0,{2/3*\h});\fill[blue!10, draw=black] (X) -- (Y) -- (Z) -- cycle;}\def\nmax{8}% nb. of triangles on each branch\newcommand{\Triangle}[1]{%\foreach \coord/\point in {#1} {\coordinate (\coord) at (\point);}\construct{A}{B}{C}}\begin{document}\begin{tikzpicture}[scale=7.0]\basetriangle\Triangle{A/X,B/Y,C/Z}\Triangle{C/X,A/Y,B/Z}\Triangle{B/X,C/Y,A/Z}\end{tikzpicture}\end{document}
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