Summary

DescriptionRabbit-lamination.png	English: quadratic invariant lamination ${\displaystyle L_{\frac {1}{7}}}$ associated with rabbit Julia set ${\displaystyle f_{c}(z)=z^{2}+c}$ where c=0.74486176661974*i-0.12256116687665 is a center of period 3 component of Mandelbrot set
Source	Made with use of program drawlam by Clinton P. Curry[1][2]
Author	Adam majewski
Other versions	Paritition of dynamic plane : Douady rabbit Julia set and external rays landing on fixed point ${\displaystyle \alpha _{c}\,}$ Orbit portrait made in hyperbolic way. Paritition of the circle by period 3 orbit ( angles under doubling map) Topological model of Mandelbrot set using Lavaurs algorith up to period 12 quadratic invariant lamination ${\displaystyle L_{\frac {1}{3}}}$ associated with basilica Julia set ${\displaystyle f_{c}(z)=z^{2}-1}$

Long description

Input file :

 rabbit.png
 2
 10
 500 500
 -1.25 1.25 -1.25 1.25
 1/7 9/14 1
 1
 1/7 2/7

How to run :

drawlam < rabbit.in

Major leaves :

Minor leaf :(1/7 ; 2/7 )^[3]

" the lamination corresponding to the rabbit is given below; it takes ten iterative preimages of the (1/7, 2/7) leaf which do not cross the (1/7, 9/14) chord. (The "True" associated with that leaf indicates that preimages are to be taken in the [1/7, 9/14) interval and the [9/14, 1/7) interval; "False" would give the opposite endpoint arrangement.)" C. Curry

References

1. ↑ DrawLam.py is a Python library which makes it easy to draw laminations
2. ↑ Drawing Poincaré Geodesics in the Unit Disk by Clinton P. Curry
3. ↑ Rational maps represented by both rabbit and aeroplane matings by Freddie R. Exall

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