We turn the data into a
sequence of 1s, 2s, 3s, and 4s. Suppose we have measured values x_{1},
x_{2}, ..., x_{N}. First,
find the range of the values, that is, find the
maximum (max) and the minimun (min)
of the x_{i}.

Next, divide the range (min, max) into four equal-size bins,
numbered 1, 2, 3, and 4. Each x_{i} lies in one of these bins, so we can
convert the sequence x_{1}, x_{2}, ... into a sequence of 1s, 2s,
3s, and 4s, called the symbol string associated with the data. (We must make
some choices if one of the x_{i} lands exactly on the between two bins. For
example, we might always take the smaller bin number.)

Now we drive the IFS with the symbol string
i_{1}, i_{2}, ..., i_{N} corresponding to the data sequence.
Start with a point **p _{0}** at the middle of the unit square. Then

T_{1}(x, y) is the midpoint of the line from (x, y) to (0, 0),

T_{2}(x, y) is the midpoint of the line from (x, y) to (1, 0),

T_{3}(x, y) is the midpoint of the line from (x, y) to (0, 1), and

T_{4}(x, y) is the midpoint of the line from (x, y) to (1, 1).

Click on the small picture to see how the symbol string above drives the IFS. |

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