# Uncovering Chaos: Precision and Iterative Processes

Hard

Ever wonder how precision affects chaos? We'll find out by testing different constants and levels of precision in an iterative process. We'll use Microsoft Excel to calculate the iterations and see how the results vary.

## Hypothesis

The hypothesis is that the constant used will have a great effect on the type of sequence that results, and that precision will have a distinct effect on the outcomes.

## Method & Materials

You will compare outcomes for different values of the constant r and different levels of precision for the iterative process x(n+1) = rx(n)(1-x(n)). Each process will be repeated for 26 iterations, starting with x(0) = 0.5.

You will need Microsoft Excel to calculate the iterations.

## Results

The experiment revealed that the constant used had a great effect on the type of sequence that resulted, and that precision had a distinct effect on the outcomes. For some constants, changing the level of rounding had such a strong effect that the same sequence would either bifurcate or converge, depending on the precision.

## Why do this project?

This science project is so interesting because it reveals how chaos appears in iterative processes with differing levels of precision.

## Also Consider

Experiment variations to consider include testing different constants and different levels of precision for the iterative process.

## Full project details

You can find additional information and details for this science fair project here. Have fun exploring!Share this Science Project:

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