IFS Driven by Texts

Driven IFS is a potentially interesting tool for analyzing patterns in data, but we need to be careful with how the data are binned. A text is a string, but in an alphabet of more than four symbols. How can we convert this into a string in an alphabet of four symbols?

One possibility is to treat words as the fundamental units of the text, and assign bins by parts of speech. Here is an example.

Another choice is to treat letters as the fundamental units and assign bins by ignoring some letters, or grouping the letters together. Here is an example.

Finding a meaningful translation of text into a symbol string suitable for driving an IFS is an intricate problem. But this is a very good feature of the driven IFS approach: it encourages experimentation with different methods, thought about open-ended problems, questions for which there are no "right" answers. In addition, as illustrated in the preceding paragraph, it can lead to good mathematical questions about the driven IFS itself.

Here are three examples of recent student projects.

Investigating the authorship of chapters of Genesis using gemantria to convert text to numbers. This is a variation on the previous example.

Comparing the sound patterns of sonnets using the soundex algorithm to convert text to numbers.

Looking for patterns of shots (distance and duration) in film.

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