simpler curves, analogous to the construction of the Koch snowflake: Start with a single line segment in the plane Repeatedly replace each line segment of the curve with three shorter segments, forming 120° angles at each junction between two consecutive segments, with the first and last segments of the curve either parallel to the original line segment or forming a 60° angle with it. At every iteration, this construction gives a continuous curve. In the limit, these approach a curve that traces out the Sierpinski triangle by a single continuous directed (infinitely wiggly) path, which is called the Sierpinski arrowhead. In fact, the aim of the original article by Sierpinski of 1915, was to show an example of a curve (a Cantorian curve), as the title of the article itself declares. Cellular automata The Sierpinski triangle also appears in certain cellular automata (such as Rule 90), including those relating to Conway's Game of Life. For instance, the Life-like cellular automaton B1/S12 when applied to a single cell will generate four approximations of the Sierpinski triangle. A very long one cell thick line in standard life will create two mirrored Sierpiński triangles. The time-space diagram of a replicator pattern in a cellular automaton also often resembles a Sierpiński triangle, such as that of the common replicator in HighLife. The Sierpinski triangle can also be found in the Ulam-Warburton automaton and the Hex-Ulam-Warburton automaton. Pascal's triangle If one takes Pascal's triangle with rows and colors the even numbers white, and the odd numbers black, the result is an approximation to the Sierpiński triangle. More precisely, the limit as approaches infinity of this parity-colored -row Pascal triangle is the Sierpinski triangle. Towers of Hanoi The Towers of Hanoi puzzle involves moving disks of different sizes between three pegs, maintaining the property that no disk is ever placed on top of a smaller disk. The states of an -disk puzzle, and the allowable moves from one state to another, form an undirected graph, the Hanoi graph, that can be represented geometrically as the intersection graph of the set of triangles remaining after the th step in the construction of the Sierpinski triangle. Thus, in the limit as goes to infinity, this sequence of graphs can be interpreted as a discrete analogue of the Sierpinski triangle. Properties For integer number of dimensions , when doubling a side of an object, copies of it are created,