9758

Plotting Julia Sets

Change the parameter for the quadratic Julia set using either the two-dimensional or one-dimensional sliders to explore endless variations of fractals. Explore the Julia set using the zoom and panning tools: dragging the "zoom" slider to the left zooms in, dragging to the right zooms out; pan in 2D using the "panning" two-dimensional slider or drag the "additional x panning" and "additional y panning" sliders for more precise control. As you zoom in and out, a very loose, rough low-resolution preview rendering of the fractal is displayed until you stop moving the slider and the display is given time to render fully. Once you have zoomed into a value less than 0.05, activate more precise zoom and panning controls by checking "fine controls". Now the "zoom" slider can zoom even closer, and the "additional x panning" and "additional y panning" sliders are more precise. Depending on how detailed a rendering you want, increase or decrease the resolution. Make the axes visible or invisible by checking the "axes" checkbox.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Please be patient! Results may take several seconds to calculate.
To improve efficiency, the lattice of points iterated for a particular view is determined by the lower and upper and bounds and the zoom level. So at a zoom level of 0.0044 on an and range of 0.008, 40401 points are generated at a density of units squared. Each point is then iterated some times proportional to the zoom level (the closer the zoom, the more iterations are required to render a detailed image; this is determined by a logarithmic function that preserves detail at very high zooms). In this way, no points are iterated that are not subsequently plotted.
Not only is the rendering of the lattice optimized to waste no processing time, it is also cached so that recalling previously seen configurations is nearly instantaneous and requires no reiteration of the lattice, only a replotting. This caching mechanism also speeds up browsing within limited areas at the same zoom level because many of the lattice points generated have been cached, and so do not need to be reiterated.
You can increase or decrease the number of iterations by specifying a resolution under "render settings"; the number selected serves as a coefficient and does not specify the number of iterations outright.
The "fine controls" checkbox under "zooming & panning" is designed to be used at small scales. Since the fractals generated are infinitely detailed, this Demonstration is designed to accommodate extremely close zooms. In order to use the "fine controls" checkbox, browse to the desired area using the two-dimensional "panning" slider and the "zoom" slider. (In order to use the additional and sliders later, do not employ them now to navigate.) Once you have zoomed in such that the "zoom" slider reads a number equal to or smaller than 0.05, activate the "fine controls" checkbox. The maxima and minima of all one-dimensional "zooming & panning" sliders ("zoom", "additional x panning", and "additional y panning") will be redefined to make the sliders more precise. The two-dimensional slider, at this point, is too coarse to use, and so to navigate with the fine controls, use the "zoom" slider and the additional and panning sliders.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+