Buddhabrot Buddhabrot
Buddhabrot 4D Applet

Just like there's Mandelbrot set explorers, I thought it would be nice to have a Buddhabrot explorer to be able to see the object from any point of view.

No Java Support.
Instruction manual

Press the mouse's primary button on the image to show the axes of coordinates. Keep the button pressed and move the mouse to shift the point of view on latitude and longitude -the 3D model is contained in a sphere-; you'll see the axes move. When you release the button, an animation will start loading to change the point of view to the new perspective through the shortest path, or the perspective will be directly painted -depends on whether the "Animación" checkbox is selected or not, on the "Animación BuddhaBrot" menu. If instead of releasing the primary button you press another one, you cancel the rotation.

The progress bar underneath the buddha shows how the animation load is doing. If you want to abort this process press the "Cancela animación" button.

  • Selección modelo 4D: You can see the Buddhabrot, the Buddhagram, the negative Buddhabrot, and the Buddhabrot's precursor ("primitive Buddhabrot").
  • Selección modelo 3D: Just like you can get 3 capital planes (x, y; x, z; y, z) from 3 dimensions, you can get 4 capital 3D objects from 4 dimensions. Here's where you can choose the one you want look at.
    The rotation from one model to another can be produced as an animation. But, what is it you be seeing? It's best to explain with an example; if we have the "Zr Zi Cr" model, Zr is represented on the X axis, Zi on the Y, and Cr on the Z. When rotating to the "Cr Ci Zi" model, the X axis that represents Zr will rotate 90º towards Cr, the Y axis will rotate from Zi to Ci, and on the Z we will see Cr rotate towards Zi.
  • Relación colores-N: Color assignation is based on how many times -n- we have to iterate the Mandelbrot functionto identify points. There's 3 color layers: red, green, and blue, and each one represents an interval of n -specifically:
    • Alta: n is between 2501 and 5000.
    • Media: between 1001 and 2500 n.
    • Baja: 500-1000 n.

    The arrow buttons by the side are used to sort the colors on the list -moves them up or to the lowest position-, and repaint the buddha.
  • Animación BuddhaBrot: The purpose of this menu is to control the animatons. This get generated by rotating the buddha, or changing the 3D model.
    • Animar: Select this checkbox to animate rotations.
    • Ángulo de rotación...: Indicates the angle in degrees that the point of view will rotate between frames. This value is an approximation; in truth, we use the closest angle to make the animation even. The angle must be between 5 and 45º.
    • Fotogramas por segundo: Adjust this value, which must be between 4 and 12, to have the animations happen slower or faster.
  • Controles animación: After preparing the animation, you can see the initial and final axes of coordinates. You control the animation playback through the typical buttons:
    • Left arrow: Jump to the last frame.
    • Central arrow: The play/pause button; starts or halts playback.
    • Right arrow: Jump to the next frame.

Naturally, each 4D model takes a different time to draw, since the only thing that changes amongst them is the render. With an Acer w/ AMD Sempron at 1.8Ghz benchmarking results were:

  • BuddhaBrot: 2-2.5 seconds.
  • BuddhaGrama: 1-1.5 seconds.
  • BuddhaBrot negativo: 3.5-4 seconds.
  • BuddhaBrot primitivo: 5-6 seconds.

Anyway, you can see how long your computer takes to render a buddha by opening the Java console (generally found in the Notifications area, next to the system clock): lines that read "Tiempo:" indicate the milliseconds it took to paint the buddha.

 
Copyright © Albert Lobo Cusidó 2006-2014