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math-image-62
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/ math-image

NAME

math-image -- display some mathematical images

SYNOPSIS

 math-image [--options]

DESCRIPTION

math-image displays some mathematical images, either in a Gtk2 GUI, as an image file output, or setting the root window.

There's lots of options for what to display, in particular including Ulam's spiral of prime numbers, and variations on the numbers in a path theme including Sacks spiral and Vogel floret. Try --random or the Randomize button for interesting combinations.

Most of the code is plain Perl, so it's not blindingly fast, but the GUI or the root window are drawn progressively so you can see what's happening. In the GUI you can change the controls while drawing to start again on something else.

Mouse button 1 in the GUI drags the image to see parts away from the origin and which otherwise wouldn't fit on screen. This can become particularly slow when displaying things like prime numbers which must be calculated all the way up to the desired part.

OPTIONS

Values Options

The following otpions control what set of values to display. The --values option described last is the most general.

--primes

The prime numbers.

--twin
--twin1
--twin2

The twin primes. --twin is both twins like 11,13. --twin1 is just the first of each like 11, or --twin2 is just the second like 13.

--semi-primes
--semi-primes-odd

The semi-prime or bi-prime numbers, meaning integers which have two prime factors p*q, including p==q squares of primes. --semi-primes-odd is just the odd semiprimes.

--squares

The perfect squares 1, 4, 9, 16, 25, 36, etc.

--pronic

The pronic numbers 2, 6, 12, 20, 30, 42, etc, k*(k+1). These are half way between successive perfect squares, and twice the triangular numbers.

--triangular

The triangular numbers 1, 3, 6, 10, 15, 21, etc, k*(k+1)/2.

--polygonal=K

The K-sided polygon numbers. For example --polygonal=3 is the triangular numbers, --polygonal=4 is the squares.

--cubes
--tetrahedral

The cubes 1, 8, 27, 64, 125, etc or tetrahedral numbers 1, 4, 10, 20, 35, 56, etc. These tend to grow too quickly to display much of a pattern, though the Vogel floret is close,

    math-image --cubes --vogel
--fibonacci

The Fibonacci numbers 1,1,2,3,5,8,13,21, etc. On the Vogel floret these fall on an axis going to the right. For other spirals and paths they tend to grow too quickly to show much.

--perrin
--padovan

The Perrin numbers 3, 0, 2, 3, 2, 5, 5, 7, 10, etc. Or Padovan numbers 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, etc. These are cubic recurrences and tend to grow too quickly to display much in the way of patterns.

--fraction=5/29
--fraction=1.234

The digits in the decimal expansion of a fraction. For example the default in the GUI is 5/29 which means 9,11,12, 17, 21,22,24, 27,28,29,30, etc. A decimal like 1.234 means 1234/1000.

A fraction is always a repeating pattern, with length no longer than the denominator, but can give interesting patterns for various paths. For example in the Corner path the fine structure constant 1/137 in binary is a repeating pattern of an angry man with a beard and a skull wearing a hat. No doubt this has deep cosmic significance.

    math-image --corner --values=FractionDigits,radix=2,fraction=1/137
--all
--odd
--even

All integers, or just odd or even integers. For the paths which fill the plane --all will just fill the screen (slowly!), but for --sacks and --vogel it shows where all the points lie.

--aronson

Aronson's sequence 1,4,9,... of "T is the first, fourth, ninth, ...". This requires the Math::Aronson module.

--expression='x^2+2*x+1'

Draw values following a formula. It should have a single variable which will be evaluated at 0,1,2, etc. This option requires Math::Symbolic.

--lines

Draw lines along the path instead of a set of selected points. This shows where a path travels but you may have to increase the --scale to see it properly.

--values=MODULE
--values=MODULE,NAME=VALUE,NAME=VALUE,...

Draw values from the given App::MathImage::NumSeq::Sequence module. For example

    math-image --values=Emirps

The names for these modules are not settled, so expect some splits, mergers or renamings. Parameters can be passed as comma separated NAME=VALUE, for example

    math-image --values=TwinPrimes,pairs=both

This can be used to read values from a text file

    math-image --values=File,filename=/my/dir/data.txt

And the OEIS module takes a sequence of values by its OEIS A-number, for example tribonnaci numbers A000073

    math-image --values=OEIS,anum=A000073

This selects whichever module implements the desired sequence, or will read downloaded OEIS files from a $HOME/OEIS/ directory,

    A000073.internal     # for info
    A000073.html         # fragile for info, but accepted
    b000073.txt          # values file, if available

A .internal file is the "internal format" OEIS info download. The .html rendition of the same works, but parsing it is likely to be fragile and may or may not work.

Path Options

The following control the path in the plane where on which the values will be displayed. The --path option described last is the most general.

--ulam

Ulam's primes in a square spiral (currently the default).

--vogel

Vogel's floret design for the positions of seeds in a sunflower (see Math::PlanePath::VogelFloret). Try the following to see all the points in the pattern before applying various special sets of values.

    math-image --vogel --all --scale=10

Scaling up helps the circles draw properly. When the values displayed are less than all the integers a lower scale can be used.

--sacks

An Archimedian spiral with the square root as angle of rotation, by Robert Sacks (see Math::PlanePath::SacksSpiral).

--theodorus

The spiral of Theodorus or square-root spiral (see Math::PlanePath::TheodorusSpiral).

--diamond

A diamond shaped spiral (see Math::PlanePath::DiamondSpiral).

--pyramid

The sides of a pyramid shape (see Math::PlanePath::PyramidSides).

--pyramid-rows

A pyramid made from horizontal rows (see Math::PlanePath::PyramidRows).

--corner
--diagonals

Corners or diagonals between the X and Y axes, per Math::PlanePath::Corner and Math::PlanePath::Diagonals.

--rows
--columns

Points drawn in successive rows or columns.

--path=MODULE
--path=MODULE,NAME=VALUE,NAME=VALUE,...

Draw following the given Math::PlanePath module. For example

    math-image --path=HeptSpiralSkewed

This includes experimental paths called "MathImageFoo", but expect their names to change when finished.

Parameters to the path are supplied as comma separated NAME=VALUE, for example,

    math-image --path=SquareSpiral,wider=3

Output Options

The default is to run the Gtk GUI.

--fullscreen

Start the GUI in full screen mode. Menu entry Tools/Fullscreen can toggle between full screen and a normal window. In full screen mode the menus still work, just press Alt-F, Alt-T, etc as normal.

--root

Set the root window background to the requested image and exit. For example a random image from your ~/.xsession file,

    math-image --root --random

Add --verbose to print what was in fact chosen and displayed. Output in ~/.xsession normally goes to the ~/.xsession-errors file. Sometimes --random may use a lot of memory, so consider a limit (see sh(1)) or timeout (see timeout(1)), or both.

Under X the root window is set with X11::Protocol if available, otherwise Gtk2. X11::Protocol is preferred as it allows --foreground and --background colours to be preserved on a PseudoColor visual. Gtk2 is fine on a TrueColor, or using black and white (those colours permanent in the default colormap), but otherwise colours won't be preserved.

--flash

Flash the requested image on the screen instead of starting the GUI. Together with --root the image is drawn to the root then flashed as well. This is good if updating the background randomly every so often, as it shows the image when otherwise obscured by lots of windows.

    math-image --root --random --flash
--display=DPY

Select the X server for X11 or Gtk output. The default is from the DISPLAY environment variable (normally set at X startup).

    math-image --display=:3
--png
--xpm

Write a PNG or XPM image file to standard output and exit. PNG is always possible with GdkPixbuf but can also use Image::Base::GD, Image::Base::PNGwriter, Image::Base::Imager, Image::Base::Magick or Image::Base::Prima::Image and their respective supporting libraries.

    math-image --png >/tmp/my-file.png

XPM output requires either Image::Xpm, Image::Base::Magick or Image::Base::Prima::Image.

Note that Prima for X11 requires an X server to do its drawing, either PNG or XPM (expect an obscure error if no display).

--text

Write a text-only image to standard output and exit. The default size follows the terminal with Term::Size. A typical tty size like 80x25 is usually too small to see much, but a bigger image might be cute to send to a line printer or similar.

    math-image --text --size=130x49 | lpr
--prima

Run the Prima GUI. This requires the Prima and Image::Base::Prima::Drawable modules. It doesn't yet have the full set of options the Gtk GUI does, but works as far as it goes.

A combination --prima --png means write a PNG image to standard output, using Prima.

--curses

Run the Curses interactive text interface. This requires the Curses::UI modules. This is experimental and the control options are minimal.

Other Options

--random

Choose a path and values at random. For example in your ~/.xsession

    math-image --root --random
--foreground=COLOUR
--background=COLOUR

Set the foreground and background colours. The colours can be either names or hex style #RRGGBB or #RRRRGGGGBBBB. For example white on a shade of red,

    math-image --foreground=white --background=#A01010

The default is white foreground on black background. For a --root background a full white can be a bit hard on the eye when there's a lot of points shown. Try a shade of grey instead

    math-image --root --foreground=lightgrey

Available names depend on the output type. Gtk uses a hard-coded copy of the X /etc/X11/rgb.txt. The X11::Protocol --root uses the server's database. --png output with GD has the GD::Simple names. --xpm passes anything at all through to the file. For --text currently the colours can be single characters to show, though perhaps that will change.

--size=PIXELS
--size=WIDTHxHEIGHT

Set the size of the image in pixels. A single value means that size square, otherwise WIDTHxHEIGHT. For --root this size is currently ignored and the full screen used.

For the GUI this is an initial size, though it might be widened to accommodate the menubar. Under --fullscreen the size is the unfullscreened window if you switch back to that (menu entry Tools/Fullscreen).

The default for the GUI is about 4/5 of the screen. The default for PNG etc image file output is an arbitrary 200x200, or for --text output the size of the terminal from Term::Size.

--scale=PIXELS

How many pixels for each value shown. The current default is 3 to show 3x3 pixel squares, or for --text output just 1 for a pixel per character

--help, -?

Print a summary of the options.

--version

Print the program version number.

--<gtk-options>

Standard Gtk options. See gtk-options(7) for the full list. The only one which does much for math-image is --display to set the X display (default from the DISPLAY environment variable).

MODULES

In addition to the modules noted above, the following are used in the GUI if available,

Gtk2::Ex::PodViewer

A "Help/POD Documentation" menu item to display this documentation and the Math::PlanePath classes.

Gtk2::Ex::CrossHair

Lines following the cursor, enabled from the Tools/Cross menu item.

Gtk2::Ex::ErrorTextDialog

Error messages in a dialog instead of to STDERR. Of course there shouldn't be any errors!

Gtk2::Ex::QuadButton

Scroll arrows in the bottom right corner.

ENVIRONMENT

DISPLAY

The X display to use.

BUGS

Some of the values plotted can be a bit slow to generate or use a lot of memory, or both. When the path goes out to large positions, or when paged out away from the origin, the display can hang generating values. This happens for example plotting primes on the PythagoreanTree.

SEE ALSO

gtk-options(7), xsetroot(1)

Math::PlanePath, Math::Aronson, Gtk2, X11::Protocol, Gtk2::Ex::PodViewer, Gtk2::Ex::CrossHair, Gtk2::Ex::ErrorTextDialog

HOME PAGE

http://user42.tuxfamily.org/math-image/index.html

LICENSE

Math-Image is Copyright 2010, 2011 Kevin Ryde

Math-Image is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-Image is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-Image. If not, see <http://www.gnu.org/licenses/>.