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Glossary of Terms

[Although I've written these definitions with the guidance of more knowledgeable people, they are (hopefully) simplified to language that most non-mathematicians can understand. If you're interested in a more technical or complex description, let me know and I'll point you toward some resources.]

  • anti-aliasing – a process that improves the quality of rendered images by sharpening and smoothening them, removing jagged edges. You can find more detailed information in the UF Help file or here.
  • bailout – Specifies the magnitude of z that will cause the formula to stop iterating. To obtain the "true" Mandelbrot set, this should be set to 4 or larger. Larger values tend to smooth the outside areas. Values less than 4 can cut off part of the fractal shape. Also called the bailout threshold.
  • cardioid – The main body of the Mandelbrot shape. See this explanation at MathWorld for a more complete description.
  • complex number – A number that has two components: a real part and an imaginary part. Mathematically, complex numbers are notated like 0.625+0.1i, where 0.625 is the real component and 0.1i is the imaginary component. In Ultra Fractal, and here in this course, that same complex number would be notated 0.625/0.1 . You can read much more about complex numbers here.
  • complex plane – Every complex number has a unique position on the complex plane. You can picture the plane like the X and Y grid we used to plot points in high school math classes. The horizontal (real) axis contains all the points in which the real component is any number and the imaginary component is 0. The vertical (imaginary) axis contains all the points where the real component is 0 and the imaginary component is any number. In the upper right quadrant of the complex plane, both the real and imaginary components are positive. In the lower right quadrant, the real component is positive and the imaginary component is negative. In the lower left quadrant, both the real and imaginary components are negative. And, finally, in the upper left quadrant, the real component is negative and the imaginary component is positive.
  • cranium spiral – spiral shapes that resemble a cranium (skull), found on the disk side of any seahorse valley. This example comes from the main disk and has two spiral arms. Other cranium spirals may have more arms, corresponding to the number of their originating disk.

  • Cranium Spiral
  • disk – The nearly circular shapes surrounding the Mandelbrot's main cardioid shape. The largest disk is sometimes referred to as the "head", and is also surrounded by smaller disks. There are an infinite number of disks in the Mandelbrot set.
  • dendrite – a twig-like branch that extends outward from any disk. The main dendrite is absolutely straight and extends westward from the main disk and forms part of the Mandelbrot Set's horizontal (real) axis. Other dendrites are curvy or jagged in shape. All dendrites have mini-Mandelbrots embedded in them. This example comes from Disk 3.

  • Main Dendrite,
    showing the West Midget

    Disk 3 Dendrites
  • elephant spiral – a spiral resembling an elephant's body and trunk found in Elephant Valley. The number of spiral arms increases as the shapes descend into the valley.

  • Elephant Spiral
  • inside point – Any point in the Mandelbrot set whose orbit stays bounded; that is, the magnitude of a z value in the orbit never exceeds the bailout threshold. In the default parameter set we use in this course, Solid Color inside points are colored turquoise.
  • iteration – One execution of the fractal formula. (Iterations (plural) – the repeated application of the fractal formula).
  • magnitude – The size of the complex number. The magnitude is never negative.
  • maximum iterations – A value set by the user to limit the number of times the fractal formula will execute (iterate) before determining whether a point is inside or outside. Lower values produce less detailed coastline structure (and larger, smoother inside areas). Larger values produce more complex coastlines and a more accurate representation of the true Mandelbrot shape, but greatly increase calculation or rendering time.
  • midget – A small, warped copy of the entire Mandelbrot set, complete with main cardioid and disks. Midgets are found on the horizontal axis to the west of the main disk, and in dendrite and spiral structures throughout the Mandelbrot set.
  • orbit – The sequence of values that results from the repeated iterations of the fractal formula.
  • outside point – Any point in the Mandelbrot set whose orbit grows unbounded; that is, the magnitudes of z values in the orbit exceed the bailout threshold. In the default parameter set we use in this course, Solid Color outside points are colored magenta.
  • pixel – Short for Picture Element, a pixel is a single point in a graphic image. Graphics monitors display pictures by dividing the display screen into thousands (or millions) of pixels, arranged in rows and columns. The pixels are so close together that they appear connected.
  • render – To perform the necessary calculations to draw the image onscreen or to a file on disk. Rendering fractals to disk is the preferred way of exporting artwork to bitmap images, ready for printing or publishing on the web.
  • scepter spiral – a special spiral shape that extends outward from another spiral shape. These are found in Scepter Valley, which is the "neck" region separating any disk's "head" from the disk. The shapes on the head side of Scepter Valley are cranium-shaped spirals from which the scepters extend. The shapes on the disk side of Scepter Valley are seahorse-shaped spirals from which the scepters extend.

  • Scepters extending from a
    Cranium Spiral

    Scepters extending from a
    Seahorse Spiral
  • seahorse spiral – a spiral shape resembling a seahorse, found on the cardioid side of any disk. This seahorse spiral is from the cardioid side of the main disk.

  • Seahorse Spiral
  • variable – A value that can be varied. The letters z and c in the Mandelbrot and Julia formulas represent values that may be changed during the iteration process.
  • west midget – the largest copy of the Mandelbrot set embedded in the main dendrite. See Dendrite and refer to the Map of the Mandelbrot Set.

  • Copyright © 2005-2011 Janet Parke