In mathematics, the boustrophedon transform is a procedure which maps one sequence to another. The transformed sequence is computed by an "addition" operation, implemented as if filling a triangular array in a boustrophedon (zigzag- or serpentine-like) manner—as opposed to a "raster scan" sawtooth-like manner.

The boustrophedon transform is a numerical, sequence-generating transformation, which is determined by a binary operation such as addition.

Generally speaking, given a sequence: ${\displaystyle (a_{0},a_{1},a_{2},\ldots )}$, the boustrophedon transform yields another sequence: ${\displaystyle (b_{0},b_{1},b_{2},\ldots )}$, where ${\displaystyle b_{0}}$ is likely defined equivalent to ${\displaystyle a_{0}}$. The entirety of the transformation itself can be visualized (or imagined) as being constructed by filling-out the triangle as shown in Figure 1.

To fill-out the numerical Isosceles triangle (Figure 1), you start with the input sequence, ${\displaystyle (a_{0},a_{1},a_{2},\ldots )}$, and place one value (from the input sequence) per row, using the boustrophedon scan (zigzag- or serpentine-like) approach.

The top vertex of the triangle will be the input value ${\displaystyle a_{0}}$, equivalent to output value ${\displaystyle b_{0}}$, and we number this top row as row 0.

The subsequent rows (going down to the base of the triangle) are numbered consecutively (from 0) as integers—let ${\displaystyle k}$ denote the number of the row currently being filled. These rows are constructed according to the row number (${\displaystyle k}$) as follows:

Refer to the arrows in Figure 1 for a visual representation of these "addition" operations.

For a given, finite input-sequence: ${\displaystyle (a_{0},a_{1},...a_{N})}$, of ${\displaystyle N}$ values, there will be exactly ${\displaystyle N}$ rows in the triangle, such that ${\displaystyle k}$ is an integer in the range: ${\displaystyle [0,N)}$ (exclusive). In other words, the last row is ${\displaystyle k=N-1}$.