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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 graphical interface, 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 don't fit on screen or in the window. This can become a bit slow when displaying things like prime numbers which must be calculated all the way up to the desired part.

OPTIONS

Values Options

The following control what set of values to display.

--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.

--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 1 bits in the binary 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 can be given so 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

    math-image --corner --fraction=1/137

shows the fine structure constant 1/137 as a repeating pattern of an angry man with a beard and a skull wearing a hat, this no doubt having deep cosmic significance.

--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 --vogely 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.

Path Options

The following control the path in the plane where the values will be displayed as pixels (or circles for Sacks and Vogel).

--ulam

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

--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 points going by their square root, 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

Diagonals between the X and Y axes, per Math::PlanePath::Diagonals.

--rows
--columns

Points drawn in successive rows or columns.

Output Options

--window

Run the Gtk GUI. This is the default.

--fullscreen

Run the GUI starting in full screen mode. Menu entry Tools/Fullscreen toggles between full screen and a normal window. In full screen mode the menus can still be used, just press Alt-F, Alt-T, etc as normal.

--root

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

    math-image --root --random

You can add --verbose to print what was in fact chosen and displayed (from ~/.xsession) output normally goes to the ~/.xsession-errors file).

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 pseudo-colour screen. Gtk2 on a true-colour screen is fine, and black and white too (being permanent in the default colormap), but other colours won't be preserved.

--display=DPY

Select the X server for X11::Protocol or Gtk. 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 or Image::Base::PNGwriter and their respective supporting libraries. XPM output requires Image::Xpm.

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

Write a text-only image to standard output and exit. The default size follows the terminal with Term::Size. A 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 --width=130 --height=49 | lpr
--prima

Run the Prima GUI. This requires the Prima module. This doesn't yet have the full set of options the Gtk GUI does, but it works as far as it goes.

--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 for the image, though it may be widened to accommodate the menubar. Under --fullscreen this size is the unfullscreened window if you switch back to that (menu 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 per 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.

--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!

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 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/>.