Fractals

The DiffEQPlotter explores graphical solutions to differential equation systems. Nine equation system families are provided - some simple algebraic systems, some ecology models, and some limit cycles. Each can be tuned by setting constants. Paired time plot and phase plot show the behavior of the system (trajectory) from any selected starting point. The phase plot also shows the "nullclines" (where the derivative of each equation is zero), and a vector field showing the tendency of the system across a grid over the plane.

Though not "fractals" software, it was developed for the same mathematics professor, Michael Frame of Yale University.

FracStats does R/S analysis and comparison to a normal distribution. It uses a time series, with or without difference processing on the input data. Also does multifractal analysis (f(alpha) curves) on time series or planar data, using either the method of moments or histogram method. Several data sets are supplied, but the main use is to paste in your own data to explore.

July 2012: Fixed pasting-my-data to work again, following Oracle/Java deciding that was a security risk. Now uses signed jars and JWS to bypass new security feature.

DrivenIFS explores data-driven Iterated Function Systems.

July 2012: Fixed pasting-my-data to work again, following Oracle/Java deciding that was a security risk. Now uses signed jars and JWS to bypass new security feature.

IFS with Memory applies selected sequences of affine transforms, subdividing an ancestral square, to generate fractal pictures. Sequence selection is in 2D or 3D.

Random IFS with Memory runs iterated function systems on an initial point. The user can set allowed/disallowed sequences of transforms in 1-step or 2-step memory.

Box Dimension explores the idea of fractal dimension by counting boxes along geographical edges. Latest version allows user to supply his own pictures.

Mandelbrot-Julia Sets explores the famous Mandelbrot Set and its associated Julia Sets. Each point on the Mandelbrot set generates a Julia set to the right. Includes Julia orbits, several color schemes, and alternate functions besides the usual z2.

I also have a simpler Flash version. This was written as an ActionScript 3 performance test.

Cellular Automata runs an assortment of 1- and 2-dimensional cellular automata, allowing the user to set the rules graphically.

Oscillator Synchronization explores coupled oscillators. Each oscillator is driven by a logistic map function, which can yield steady state, periodic, or chaotic behavior depending on its parameter s. Many different neighborhood coupling, initial value, and s distribution schemes are provided to explore.

FracDyn explores iterated function dynamics via 6 different analytic plots - graphical iteration (with animation), binned histogram, return map, Kelly plot, time series, and bifurcation diagram.