Q&A for How to Plot the Mandelbrot Set By Hand

Return to Full Article

Coming soon

Add New Question

Question

Why use the absolute value to find C?

Community Answer

C is acquired from Zn+1=(Zn)^2+C. Zn is the starting point, which is (0,0i) in this case, so C is always the value of Zn+1. The absolute value is used to check if the point escapes from the set. When it escapes the first time, it is considered Pass 1.

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 13 Helpful 6
Question

Why do I obtain the same results while calculating the absolute values of (-1,1) and (1,1), while in the example above (-1,1) escapes after 3rd pass and (1,1) after second?

Community Answer

In [-1, 1] (i-1), the absolute value of the third pass is equal to 2, and it escapes on the pass that it's either equal or bigger than 2, and it's equal to 2. So it goes on the third pass. In [1, 1] (1+i) you calculated it incorrectly.

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 1 Helpful 2
Question

If a cell escapes the second pass, is the cell automatically in the third pass?

Community Answer

If the cell escapes (has a value greater than 2) in the second pass, it is colored in. Any cell that does not escape in the second pass automatically gets a third pass.

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 2 Helpful 4
Question

How do I know what formulas to use? And what color to color them?

Community Answer

This particular formula has been used by Benoit Mandelbrot, but there are a plethora of others. Julia sets, 3D Mandelbrot sets use similar but different formulas. All are based on the same convergence principle. As for the colors, they are perfectly arbitrary, the colormap that you use is based on esthetical rather than mathematical reasons. Get some software for generating Mandelbrot sets and you will see all (or at least many) the possibilities.

Thanks! We're glad this was helpful.
Thank you for your feedback.
If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
Yes No

Not Helpful 7 Helpful 2