In this chapter we're going to check out what I call a 'pinch off'. By this I'm referring to the two thin peninsulas of froth which nearly separate atoms. Pinch offs are considered infinitely thin. Below, picture T1, follow red arrow to see area magnified in picture T2.
Here we are looking at a piece of the pinch off peninsula. Note the ordered arrays of atoms and their froth on either side of the peninsula. Next, picture T3 below, let's take a look at one of the atoms and its froth within the peninsula (region in red square in T2).
Here's the peninsula atom outlined above (picture T3 below). Look how the froth tails are tightly coiled about the points they orbit. Arrow T4 points to the break molecule. Note chain of froth containing the break molecule is pointing in opposite direction of the pinch. This is normal. Also note how the rest of the froth is twisted - the froth 'stem' (arrow T5) follows an 'S' shape.
Also note how the number of arms comprising the froth have increased (from atom T1) and the froth lines have grown more convulted.
The greatest asymmetry is found within the break molecules in pinchoffs. It seems the further one follows the infinitely thin pinch down the greater the asymmetry becomes. In picture T5 below, notice how the entire shape of the break molecule is warped, with the right half of the main cardioid being much larger. It almost seems like a tidal effect, as the half of the cardioid nearest the peninsula edge bulges towards it. The many (much) smaller molecules around the break molecule do not show the same degree of assymetry.
I wonder if the relative size of the break molecule to the area of the mandelbrot set on the edge of the peninsula has something to do with it. If anyone has any light to shed on this drop me an email.
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Finally here's the closeup of the stem molecule in picture T3, with negative.
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