member since June 13, 2009
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portfolio of
Claudio Gonzales

Determinant Fractal

Generates a fractal based on visualizing the call-stack of a square matrix determinant algorithm, utilizing the O(n!) method taught to students in most linear algebra courses.

Mouse x-coordinate controls the angle range of branches from individual nodes; y-coordinate controls the perspective of viewing the nodes themselves. Press spacebar to toggle node drawing, and use arrow keys to increase/decrease size of matrix being evaluated.

Field Line Analysis

An applet which allows the user to place and rotate permanent magnets (by clicking and holding the left mouse button), as well as release test particles to trace the field vectors of the ensuing system (with a right click). Pressing spacebar causes the applet to display the environment's vector fields.

Powered Buddhabrot Generator

A fractal generator which seeds a random power between 1.5 and 4.0 to mutate the buddhabrot, using speed-rendering methods explored in my other applets. Click to alter zoom level, press enter to view seeding source points.

Monopole Interaction

Similar to the particle interaction applet, this program allows the user to create a positively charged particle with a left click and a negative one with the right. Red lines indicate repulsion, blue attraction.

Particle Interaction

A program allowing you to form up to 15 particles (click and hold to create objects with greater mass) using your mouse, and observe the way in which they attract or repel one another (toggle a right mouse click). Increase speed (useful for stagnant fields or when particles are too bunched together) by scrolling up, decrease (useful for when things start moving too chaotically) by scrolling down. Press any key to freeze/unfreeze time, allowing you to set up fields without premature interaction.

Mandelbrot Explorer - Hypercomplex

Offers a new way to explore the Mandelbrot set, using the j and k dimensions of the hypercomplex number to do so. Use arrow keys to control dimension, and click left/right to zoom in/out. Push spacebar to restore the original fractal.

Note: Most of the really cool patterns I've found were made by upping the j dimension a bit while leaving k at 0, then zooming into the resulting openings between the "bulbs" of the traditional Mandelbrot set.

Julia Explorer

A port of an old C++ project from programming class my freshman year; it allows the user to sift through the infinite Julia set possibilities using their mouse coordinates, then to explore a chosen fractal by clicking.

Press any key to activate exploration mode, or to reset to scanning mode.
Click left to zoom in (when exploring), right to zoom out.

Galactic Dust

An extension of my Swarm projects into three dimensions, with some new special effects thrown in.

Click left or right to attract/repel particles (respectively).
Press the space bar to reset the particles in one of five ways, press enter to toggle tracing function.

Buddhabrot Generator

An applet which renders the Buddhabrot (a variant of the M-set) using the Metropolis-Hastings algorithm (adapted from code by Alex Boswell) and a mapping system to allow quick exploration of the fractal via zooming. Press ENTER to view source points (brighter sectors are feeding more points). Based off of a baseline rendering applet by Jared Tarbell.

Gravity Pulsar

A new application of my gravity well program, which utilizes new launching techniques to create radically different pulse-like patterns. Regenerate with a mouse click (left for a fluid release, right for a more stylized reaction).

Newton-Buddha Method

A quick sketch of a new idea using a variation of the Newton fractal but rendered via the Buddhabrot method, demonstrating the path of points as they zero in on the chosen equation's roots (ƒ(Z) = Z³-2Z²+2). Thanks to, as well as the idea and the entire Buddhabrot method from, Melinda Green.

This is just a quick proof-of-method rendering applet; a later version will be written that will involve speed-zooming and more creative coloring, as per my buddhabrot applets.

Mandelbrot Tracer

Allows the user to pick seed points (left click), tracing their orbit through the "Mandelbrot Mill". By right clicking, the background switches from a Mandelbrot fractal to a Buddhabrot fractal, which is created by the amount of times all points in the region spiral in or out of the mill.

Gravity Swarm Mark II

A second version of my Gravity Swarm sketch, which takes into account the distance between the particle and the attraction point, though not quite as much as the true relationship in nature. Uses a new coloring algorithm which is dependent on the activity level of the individual particle... controls are the same as the first version, left click to attract and right click to repel. Additionally, invert the colors with shift and toggle tracers with enter.

Happy Fourth!

Inspired by the fireworks of the Fourth. Click to invert colors. Go America!

Nebulabrot Generator

An applet which renders a Nebulabrot, with zoom-algorithms from my Buddhabrot Generator. The Nebulabrot is three buddhabrots, rendered at different bailout values, which are rendered at Red, Green and Blue and then overlaid. The applet displays the bailout values for each color layer.

Gravity Swarm

A similar sketch to my gravity well, but the particles' gravity attraction are no longer affected by the distance between them and the gravity well's center. Additionally, the well is now activated/deactivated and placed by the user's mouse click.


A simple program that reads your system clock and presents it to you... with style!

Gravity Well

A particle simulator which utilizes a baseline class (which features gravity) based on 2D vectors. Click with the left to launch the particles again, click with the right to launch them in a more unified formation.
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submitted sketches to:
Fractals & Landscapes
2D Simulations


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