| Chaos and Fractals in Financial Markets, Part 1 | The rolling of the golden apple. I meet chaos. Preliminary pictures and poems. Dynamical systems. What is chaos? I'm sensitive, don't perturb me. Why chaos? How fast do forecasts go wrong?--the Lyapunov exponent. Simple calculation using a Lyapunov exponent. Enough for now. Problems. |
| Chaos and Fractals in Financial Markets, Part 2 | The French gambler and the pollen grains. The square root of time. Normal versus lognormal. How big is it? History's first fractal. Fractal time. Probability is a one-pound jar of jelly. Problems and answers. |
| Chaos and Fractals in Financial Markets, Part 3 | Hazardous world. Coin flips and Brownian motion. A simple stochastic fractal. Sierpinski and Cantor revisited. Blob measures are no good. Coastlines and Koch curves. Using a Hausdorff measure. Jam session. |
| Chaos and Fractals in Financial Markets, Part 4 | Gamblers, zero-sets, and fractal mountains. Futures trading and the gambler's ruin problem. An example. Gauss versus Cauchy. Location and scale. |
| Chaos and Fractals in Financial Markets, Part 5 | Louis Bachelier visits the New York Stock Exchange. Bachelier's scale for stock prices. Volatility. Fractal sums of random variables. Some fun with logistic art. Julia sets. |
| Chaos and Fractals in Financial Markets, Part 6 | Prechter's drum roll. Symmetric stable distributions and the gold mean law. The Fibonacci dynamical system. |
| Chaos and Fractals in Financial Markets, Part 7 | Grow brain. Hurst, hydrology, and the annual flooding of the Nile. Calculating the Hurst exponent. A misunderstanding to avoid. Bull and bear markets. |
| Chaos and Fractals in Financial Markets, Part 8 | The Correlation Integral and the Correlation Dimension. |