Driven IFS and Data Analysis

IFS Driven by Financial Data

Part of the problem with the previous graph comes from the large range of values.
The bins are determined by the entire range, and about the first half of the values fall in the first bin.
Although it is not widely advertised, graphs of long-term financial data account for this problem by plotting the logs of the closing prices, instead of the closing prices themselves. (This is apparent if the vertical scale is shown on the graph: the space between $10 and $100 is the same as the space between $100 and $1000.)
Here is a graph of the logs of the closing prices, and the IFS driven by this sequence.
Logs of closing pricesDriven IFS
This isn't a lot better. The points along the diagonal are spread out a little more, but that is not espcially useful.
We see the same backwards Z as in closing price graph.
The main interpretation of this graph is that changes occur within a bin or between adjacent bins.

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