Learning Your Way Around

Adding Periodicities

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Now we're going to explore the periodicities of the bulbs in between any two bulbs. There is a simple and elegant rule:

The periodicity of the largest bulb in between any two bulbs is the sum of the surrounding bulbs' periodicities.

So the largest bulb between the Period 3 bulb and the Period 5 bulb has a periodicity of 8. Zoom into the bulb labeled '8' and count the arms to verify that this is the case.

Likewise, the largest bulb between the Period 5 and the Period 7 bulb is 12. Verify that this is also true.

Does this same rule apply on the other side of the Period 3 bulb, where the periodicities increase by 1 for each major bulb? Find out below!

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What is the periodicity of the largest bulb in between the Period 3 and the Period 4 bulbs [ ]
What is the periodicity of the largest bulb in between the Period 4 and the Period 5 bulbs [ ]
What is the periodicity of the largest bulb in between the Period 5 and the Period 6 bulbs [ ]

The numbers at the bottom of the Mandelbrot window show the location and magnification of the image. (X,Y,mag)
Paste in the X and Y coordinates of the the Period 10 bulb: [ ]

Next, we will put together the rules we've learned so far to allow you to discover patterns within the Mandelbrot Set that have any desired periodicity, branching and twistedness.