Very specific but easy Mandelbrot question

[Vicarious]

In the Mandelbrot set common depiction, what is the behavior of the area where the large circle and cardioid connect? At first glance, it appears that the two spikes are not connected. However, you can zoom in and increase the iterations, and the spikes get longer and longer and thinner and thinner. I wonder if it is possible to observe the very middle of this situation. What would it look like? Well, from my little bit of reading I know that all points on the X axis are included in the Mandel set. So, there is a tangent point between the circle and cardioid. The spikes never meet, and they become infinitesimally thin as you approach the tangent point. Still, I wish I could see this with my eyes. Anyone else fascinated by Mandelbrot? I don't really get how it is a set of Julia sets.

[TheBigDog]

Welcome to Hypography! I have a thread here dedicated to exploring the Mandelbrot set, and have even post some software for that very purpose.

 

http://hypography.com/forums/physics-mathematics/5980-fractal-explorations.html

 

I don't think they ever touch no matter how far you zoom in, but this will let you try and find out. :lol:

 

Bill

[Vicarious]

Big Dog! I have downloaded your fractalator, and I think it is quite an accomplishment on your part. I am excited to zoom in as far as you mentioned. However, in order to do so, I think I have to increase the iterations as I zoom. Otherwise I think the fractal is not displayed with infinite complexity. How can I do this?

 

 

Regarding the Mandelbrot, I also doubt the spikes between cardioid and circle touch. I still wonder what the link between circles and the main cardioid is like at a small scale. Are the shapes connected by a single tangent point, or is there a range of black (inside the set) above and below where the tangent point would be?