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Cubic Mandelbrot Set Images

The cubic Mandelbrot set comes from iterating z = z³+c. The basic structures are the same as in the regular Mandelbrot set but everything has 3-fold symmetry.

Calculating images of the cubic Mandelbrot set takes significantly more work than the quadratic version because more multiplications and additions are involved. For that reason, not many animations have been made with it.

Two deep-zoom animations have been published on this site so far:

• QBIX is a really nice 5000-frame high-definition deep-zoom animation published in June 2010
• this older one is a short non-deep animation created in 2005

The cubic Mandelbrot set resembles, but it definitely different from, the tricorn ("Mandelbar") fractal. Both have three-fold symmetry at low magnifications, but the tricorn fractal is fundamentally a second-order structure, and it contains mini-brots that are exactly the same as the usual second-order mini-brots, while the cubic Mandelbrot set only has third-order mini-brots.

	Feb 16, 2002 346x331 This is the first cubic polynomial image I can find saved in my collection. There are a few others from the same date.
	Feb 16, 2002 1280x1024
	Feb 16, 2002 648x538
	Feb 16, 2002 639x562
	Feb 18, 2002 640x512
	Mar 26, 2003 400x400
	Mar 26, 2003 600x600
	Jun 2, 2007 3000x2400 Unfortunately the raw data file with the location and size is lost, so I'm not sure if it is a deep-zoom, although it looks like it probably is.

Note on size and magnification: The sizes here (and on the Animations page) are the actual size of the smallest dimension of the image (usually vertically) in the complex number plane. Some programs describe image sizes by "magnification" which is usually related to the reciprocal of the image size. A size of, say, 1E-100 corresponds to a magnification of 1E+100. Some software uses the half-height of the image, so there may be an additional factor of two involved in conversion.