NESTED_SEQUENCE_DISPLAY
Display a Nested Set of Sequences

NESTED_SEQUENCE_DISPLAY is an executable MATLAB program which displays a set of sequences, as lines of X values, "stacked up" in the Y direction. For cases where successive sequences share a value, a red vertical line is drawn to highlight this.

The purpose of the plot is to emphasize the structure of a nested sequence, although it is not actually necessary for the sequences to be related in any way.

The kind of plot we are thinking of though, might look something like this:

    Sequence 4: 1    3    5  6  7  8
                |         |     |
    Sequence 3: 1         5     7
                |               |
    Sequence 2: 1    3          7
                |
    Sequence 1: 1
      

For example, the program could be used to show the nesting of the family of Clenshaw Curtis points, when choosing orders 1, 3, 5, 9, 17, 33, 65, ...

Usage:

nested_sequence_display invokes the program. It then engages in a dialog with the user, who is asked to enter, one by one, the names of files containing the sequences. When there are no more files to enter, the user should enter 'RETURN'. At that point, the plot will be drawn.

Related Data and Programs:

SEQUENCE_STREAK_DISPLAY is a MATLAB program which reads a file containing a sequence, and draws a "streak" plot in which, as each value joins the sequence, it starts a streak on the plot.

TABLE is the format used for the files containing the sequences.

Source Code:

• nested_sequence_display.m, reads a list of files containing sequences and draws a plot that highlights any nesting between successive sequences;

Examples and Tests:

CC is a set of files containing Clenshaw Curtis abscissas.

• cc01.txt, the abscissas for the rule of order 1.
• cc03.txt, the abscissas for the rule of order 3.
• cc05.txt, the abscissas for the rule of order 5.
• cc09.txt, the abscissas for the rule of order 9.
• cc17.txt, the abscissas for the rule of order 17.
• cc33.txt, the abscissas for the rule of order 33.
• cc65.txt, the abscissas for the rule of order 65.
• cc.png, a PNG image of the sequences that highlights their nesting.

You can go up one level to the MATLAB source codes.