Project and Gallery Files

Below, you will find Phaser Project and Gallery files for you to load over the Internet, or, alternatively, to download and run locally in Phaser. You are welcome to submit new projects and galleries of general interest for inclusion. Further information on Project and Gallery files is available on the Gallery tour page of this site. Additional project simulations are available in our free and growing collection of teaching modules.

To open a Phaser Project File over the Internet, start Phaser and then:

To open a Phaser Gallery File over the Internet, start Phaser and then:

If you prefer, you can download a desired file to your machine by clicking on the name of the file and then load it into Phaser locally. Follow the same steps as above, except use the menu entry Load Phaser Project or Load Gallery (or double-click on, or drag the files onto their respective application windows).

Phaser Project Files (*.ppf)

rikitake.ppf rikitake.ppf:

Rikitake coupled dynamos modeling chaotic reversals of Earth's magnetic field. This ordinary differential equation (ODE) project is used in Tutorial 5 of Phaser Help. Further mathematical details on the Rikitake two-disk dynamo system can be found in Cook and Roberts [1970] and Robbins [1977]. Information about dynamos and earth's magnetism is available at

henon2-bif.ppf henon2-bif.ppf:

Bifurcation Diagram in Phaser of one version of the classic Henon MAP (difference or recurrence equation). The solution is plotted against one of its variables x1 [-0.088, -0.083] and one of its parameters a, sampled at 1000 equal intervals between 1.14702 and 1.14706 (with each sample undergoing 7500 iterations of the map). Parameter b is fixed at 0.3. Regarding the dynamics, this chaotic exhibiting system appears to have period-halving in addition to period-doubling bifurcations.

tutorial10.ppf tutorial10.ppf:

The Phaser Project created in Tutorial 10 of Phaser Help. Real-time rotations of two solutions of a pair of Harmonic Oscillators ODE's in the Phase Portrait View. This is a conservative system, bound by a Hamiltonian function. On the geometric side, global dynamics of harmonic oscillators possess a surprisingly rich structure. The best known pictures of this system are the orthographic projections of solution curves onto the (x1, x2)-plane (configuration space) called Lissajous figure.

Phaser Gallery Files (*.pgf)

tutorial6.pgf tutorial6.pgf:

The Phaser Gallery created in Tutorial 6 of Phaser Help. A collection of phase portraits of the area-preserving Cremona MAP. Investigated and illustrated here are certain bifurcations in the dynamics of this system by plotting the solutions to the map as we vary one of its parameters. Despite its simplicity, Cremona MAP possesses very complicated dynamics reminiscent of non-integrable Hamiltonian systems.

sk-ifs.pgf sk-ifs.pgf:

A Phaser Gallery of Phase Portrait Views of curves with fractal (similarity) dimension ranging from 1.1 to 1.9. Evidenced here is a sequence of amazing curves, from a near line segment to snowflakes to a space filling curve, with an Iterated Function System (IFS) -- generated using the Sierpinski-Knopp (IFS) MAP, one of many landmark equations included in Phaser's Equation Library. The classic Koch Snowflake Curve Fractal, also known as the Koch Island, has dimension 1.2619.

icons.pgf icons.pgf:

A Phaser Gallery of Icons (Sanddollar, French Glass, Swirling Streamers, Mayan Bracelet) using Symmetric Icons MAP -- chaotic icons with dihedral or cyclic symmetry. As the complex function defined system parameters are varied, the Symmetric Icons MAP exhibits a multitude of symmetric attractors. Feel free to experiment with this system in Phaser, creating and perhaps discovering new icons!