Angles and Rays of M and J sets






Angles in parameter plane:
Of course every point of 2D plane ( complex number) has another angle = Argument.


So we have 4 types of angles:

Angle is a real number.
angle = Argument ( complex_number)
Argument ( c) : C --> R
because :
c :=  Re(c) + Im (c)* i  =
Log(c) := Ln ( r ) + i * ( angle + 2 * Pi* k )
Argument(c) := ImLog ( c) )

Angles can be measured in degrees, radians and turns.
360 [degrees] = 2 * Pi [radians] = 1 [ turn]
angles are measured in counterclockwiserotation
and modulo 1
it means 0,2 = 1,2 mod 1 = 2,2 mod 1

Forms of angles:

Ray is a set of points with the same (external or internal) angle.
It is a curve, sometimes a line.
External ray of Mandelbrot set is called parameter ray because it is on parameter plane.
External ray of Julia set is called dynamic ray because it is on dynamic plane.
R(c,angle)  = { c | Arg  M(c) = angle }
Rays are labeled by the coresponding angles.


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Autor: adammaj1-at-o2-dot--pl
Adam Majewski
Feel free to e-mail me. (:-))

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