Vortex is a program for viewing and analyzing the number spiral.

The program allows you to draw graphs like the ones on this website. It has both a graphical and command-line interface.

To install, unzip the downloaded file to the desktop or any folder. There's no installation program. To start the program, double-click it with the mouse.

If Vortex seems to stop working because you zoomed out too far, delete the "vortex.settings" file in the program's directory and restart.


The program hasn't been optimized for speed, so it may run slowly, especially on older machines with small amounts of memory. To make it run as fast as possible, keep the view zoomed in and turn off as many graph features as possible.

To report bugs, please use the "Report bug" button in the program or send email to rob @ numberspiral.com.

The program is free. To download, click the link in the box at the right.

Beta Version. 0.0.9 Build 13

Requires Windows 2000, XP, or Vista.

 Vortex graph window
Home (default zoom and go to zero) H or Home
Menu right click
Number menu shift right click on a number
Save screenshot to file F11
Go to Zero 0 (That's a zero.)
Default zoom Z
Go to cursor Ctrl left-click
Go to number N
Select number Double left-click
Command window C
Settings window S
Slide graph Arrow keys or drag with mouse. Hold Ctrl to go faster.
Clear graph Esc
Zoom in or out Mouse wheel or PgUp and PgDn. Hold Ctrl to go faster.
Draw a curve Select three numbers with double left-click, then type G.
Help F1

 Vortex command window

S ± <n> or
P ± <n>

Shows curves offset from squares or pronics..

Use these commands to display product curves as shown on the website. For example, if you type:

s   –   4

you'll see the curve which is parallel to the squares with 5, 12, 21, etc.

You can display the same curve with the coe command by typing:

coe   1   0   –4

The coe command is more powerful but a little more complicated to use.

mod <a> <b>

Shows congruence class.

This command highlights all numbers in the spiral that are congruent to a modulo b.

For example, if you enter

mod  2  5

The program will draw a green circle around every number n such that

coe <a> <b> <c>

Analyzes sequence and, optionally, draws associated curve.

Enter the three coefficients of a quadratic formula. (All the offset curves on the website are quadratic). Press "do it" to analyze the generated sequence in the command window. Press "graph it" to draw the formula's curve in the graph window.

For example, if you type:

coe   4   –8   41

you will see the curve for the quadratic formula:

4x2  –  8x  +  41

seq <n1> <n2> <n3>

Analyzes sequence and, optionally, draws associated curve.

This does the same thing as coe, except you enter any three successive numbers from the sequence instead of the formula's coefficients. (You can also do the same thing in a third way, by double-clicking three numbers on the graph and pressing G.)

For example, if you type:

seq  16  25   36

you will see the curve for the perfect squares.

ang <fraction | denominator>

Shows angle lines to help visualize offset curves.

You can type either a fraction or a whole number as the argument. A fraction designates an angle in rotations. For example, if you enter

ang 1/4

a line will be drawn 1/4 of the way around the spiral on the 90-degree line.

If you enter a whole number, a line is drawn for every fraction that has that number as a denominator. For example, if you type

ang 5

the program draws lines at 0/5, 1/5, 2/5, 3/5 and 4/5 rotations.

off <fraction [quantity]>

Shows offset curves for any given angle.

This command draws offset curves for the specified angle. (In this program, an angle is described as a fraction of a rotation. For example, 180 degrees is 1/2.) For example, this command:

off 3/7 100

draws the first 100 offset curves that are parallel to (and counterclockwise from) angle 3/7.

If you omit the quantity, the program displays the first 30 offset curves by default. For example, this command:

off 19/34

draws the first 30 offset curves that are parallel to angle 19/34.

Be careful with large denominators and large quantities; your computer may bog down and take a long time to draw the screen.

Offset curves are shown in three colors: gray indicates curves that contain primes; red indicates curves that are purely composite (except for the first and possibly second memberr) due to the fact that the sequence is "even"; and blue shows curves that are purely composite (except for the first and possibly second members) because the fractional part of their distance from the angle contains a perfect square in the numerator.

fac <n1 n2>

Shows factorization in form of intersecting curves.

Fac stands for factors. This command draws two offset curves (one product curve, one factor curve) for the specified numbers.

For example, if you want to see the curves for the multiplication 71 x 1832, you would type:

fac  71  1832

and a pair of curves will be drawn on the graph.

Clear Clears the screen
Esc Clears the command line.