atom.h File Reference

(v16)

Mandelbrot set atom finding. More...

#include <mpfr.h>
#include "utility.h"

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Functions
int	crosses_positive_real_axis (const mpfr_t ax, const mpfr_t ay, const mpfr_t bx, const mpfr_t by)
	Check if a line segment intersects with the positive real axis.
int	surrounds_origin (const mpfr_t ax, const mpfr_t ay, const mpfr_t bx, const mpfr_t by, const mpfr_t cx, const mpfr_t cy, const mpfr_t dx, const mpfr_t dy)
	Check if a square surrounds the origin.
int	did_escaped (const mpfr_t x, const mpfr_t y)
	Check if a point escaped.
unsigned int	boxperiod (const mpfr_t cx, const mpfr_t cy, const mpfr_t r, unsigned int maxperiod, void *abort_data, abort_t abort_fn)
	Find the lowest period of any atom inside a box.
int	muatom (int period, mpfr_t x, mpfr_t y, mpfr_t z, void *abort_data, abort_t abort_fn)
	Find an atom of a given period.

Detailed Description

Mandelbrot set atom finding.

Definition in file atom.h.

Function Documentation

unsigned int boxperiod	(	const mpfr_t	cx,
		const mpfr_t	cy,
		const mpfr_t	r,
		unsigned int	maxperiod,
		void *	abort_data,
		abort_t	abort_fn
	)

Find the lowest period of any atom inside a box.

Uses the Jordan curve method described here: http://mrob.com/pub/muency/period.html.

Parameters

cx	The real part of the box center.
cy	The imaginary part of the box center.
r	The box radius.
maxperiod	The maximum period to check until.

Returns

0 if no period was found, otherwise the found period.

Definition at line 87 of file atom.c.

References did_escaped(), and surrounds_origin().

Referenced by fpxx_start().

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int crosses_positive_real_axis	(	const mpfr_t	ax,
		const mpfr_t	ay,
		const mpfr_t	bx,
		const mpfr_t	by
	)

Check if a line segment intersects with the positive real axis.

Parameters

ax	The x coordinate of the first point.
ay	The y coordinate of the first point.
bx	The x coordinate of the second point.
by	The y coordinate of the second point.

Returns

1 if \((a,b)\) intersects \((0,+\infty)\), 0 otherwise.

Definition at line 23 of file atom.c.

Referenced by surrounds_origin().

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int did_escaped	(	const mpfr_t	x,
		const mpfr_t	y
	)

Check if a point escaped.

This is a cheap inaccurate check using exponents. Inf/NaN are assumed escaped.

Parameters

x	The real part of the point.
y	The imaginary part of the point.

Returns

1 if the point escaped, 0 otherwise.

Definition at line 71 of file atom.c.

Referenced by boxperiod().

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int muatom	(	int	period,
		mpfr_t	x,
		mpfr_t	y,
		mpfr_t	z,
		void *	abort_data,
		abort_t	abort_fn
	)

Find an atom of a given period.

Uses Newton's method as described here: http://mathr.co.uk/mandelbrot/bonds.pdf. The method is iterated with increased precision until the nucleus and \(\frac{1}{2}\) bond are distint, which gives a size estimate and ensures the nucleus has sufficient precision.

Parameters

period	The period of the nucleus.
x	The real part of the nucleus (input: guess, output: nucleus).
y	The imaginary part of the nucleus (input: guess, output: nucleus).
z	The size of the nucleus (output valid when 1 is returned)

Returns

1 if the nucleus was accurately determined, 0 otherwise.

Definition at line 151 of file atom.c.

References VARS.

Referenced by fpxx_start().

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int surrounds_origin	(	const mpfr_t	ax,
		const mpfr_t	ay,
		const mpfr_t	bx,
		const mpfr_t	by,
		const mpfr_t	cx,
		const mpfr_t	cy,
		const mpfr_t	dx,
		const mpfr_t	dy
	)

Check if a square surrounds the origin.

Parameters

ax	The x coordinate of the first point.
ay	The y coordinate of the first point.
bx	The x coordinate of the second point.
by	The y coordinate of the second point.
cx	The x coordinate of the third point.
cy	The y coordinate of the third point.
dx	The x coordinate of the fourth point.
dy	The y coordinate of the fourth point.

Returns

1 if \((a,b)(b,c)(c,d)(d,a)\) surround \(0\), 0 otherwise.

Definition at line 54 of file atom.c.

References crosses_positive_real_axis().

Referenced by boxperiod().

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