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THE LOTUS BOARD:

NOTATION AND DIRECTIONAL CONCEPTS

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Copyright (c) 1998

by david moeser

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TABLE OF CONTENTS
=================

CHAPTER I:  INTRODUCTION
========================
1.0  Overview
2.0  General Information
2.1  Chess Variants Information

CHAPTER II:  NOTATION AND THE BOARD
===================================
3.0  Basic Concepts for Chess Notation
3.1  X-axis Ranks
3.2  Wavy Ranks
3.3  Y-axis Files
3.4  Other Files for Notation
3.5  Algebraic Notation
3.6  The Entire Board
4.0  Constructing an Actual Board
4.1  Triangles
4.2  Squares

CHAPTER III:  VECTORS
=====================
5.0  Vectors: The Four Axes
5.1  The X-axis
5.2  The Y-axis
5.3  The Z-axes (1)
5.4  The Z-axes (2)
5.5  The V-axis
5.6  The W-axis
6.0  Orthogonality
6.1  Superorthogonality

CHAPTER IV:  PATTERNS
=====================
7.0  Rows (and Ranks)
7.1  Files
7.2  Diagonals
8.0  Lotus Paths
8.1  Lotus Path Movement
8.2  Lotus Circles
8.3  Other Lotus Patterns
9.0  Other Patterns
9.1  Triangles
9.2  Squares
9.3  Hexagons

CHAPTER :I:  INTRODUCTION
=========================

1.0  OVERVIEW
=============

Lotus-39 is a chess game played on a lotus board consisting of 39
squares, called cells.  The rules of the game are substantially the
same as Regular Chess.  Except for one piece, Lotus-39 uses established
chess pieces used in the present or past in Regular Chess, and
the movements of the pieces are as analogous to the concepts of Regular
Chess as possible.  A regular chess set can be used.

2.0  GENERAL INFORMATION: VERSION 1.2
=====================================

Lotus-39 Chess was invented by David Moeser of Cincinnati, Ohio,
USA, in June 1998 for submission in the 1998 Chess Variants Contest.
This article is being published as of November 30, 1998, along with
other articles detailing additional aspects of Lotus Chess.  Titles
included in this set are:

1. LOTUS-39 CHESS.  Rules for playing the game.  (See file
for Version 1.0)

2. THE LOTUS BOARD: NOTATION & DIRECTIONAL CONCEPTS.  This
article, with details on these subjects:
*  Notation for the lotus board.
*  Vectors and directional concepts.
*  Orthogonality and superorthogonality.
*  Patterns and pathways for movement of pieces: rows, ranks,
files, diagonals, lotus paths, lotus circles, and other patterns.
*  Other aspects of the board, such as the color scheme used
on actual boards.

3. CHESS PIECES IN THE LOTUS ENVIRONMENT.  Explains and
illustrates the rules for movement of more than two dozen chess
pieces as used on the lotus board.  (See file for Version 1.0)

2.1  CHESS VARIANTS INFORMATION
===============================

Interested chessplayers may contact the inventor at the internet
e-mail address: erasmus at iglou dot com.  NEUE CHESS: THE BOOK, a
compilation of more than 50 pages published in Cincinnati chess
periodicals on the subject of chess variants, is available from the
author for US \$5.  (U.S.A. addresses only.  Correspondents outside
the U.S. should contact the author for shipping cost.)

The world capital of chess variants is located on the web at:
http://www.chessvariants.com/index.html.

CHAPTER :II:  NOTATION AND THE BOARD
====================================

3.0  BASIC CONCEPTS FOR CHESS NOTATION
======================================

This section introduces the chessplayer to the concepts of the
X-axis and Y-axis so that the standard notation system as used in
Regular Chess can be explained.  More details about axes will be
presented later in this article.

(NOTE: While the ASCII text Diagrams used here do a fairly good
job of illustrating the X- and Y-axes, they distort the other axes
as well as the relative sizes and relationships of some of the cells
of the lotus board.  This article will generally ignore such distor-
tions.  Chessplayers are encouraged to construct real boards so they
can follow the concepts mentioned in this article without having the
distortions and limitations of the ASCII text display.  See the sec-
tion dealing with real boards.)

DIAGRAM 3-1: X-AXIS RANKS
=========================
______
/\    /\
/    \/    \
/\    /  \    /\
/____\/      \/____\
| 6  |   6    | 6  |
|____|        |____|
/\    /\      /\    /\
/    \/    \  /    \/    \
/\    /  \    /\    /  \    /\
/____\/      \/____\/      \/____\
| 4  |   4    | 4  |   4    | 4  |
|____|        |____|        |____|
\    /\      /\    /\      /\    /
\/    \  /    \/    \  /    \/
\    /\    /  \    /\    /
\/____\/      \/____\/
| 2  |   2    | 2  |
|____|        |____|
\    /\      /\    /
\/    \  /    \/
\    /\    /
\/____\/

In Diagram 3-1 above, three horizontal rows of cells ("ranks")
have been marked: the second ("222"), fourth ("444"), and sixth
("666").  These are true (orthogonal) X-axis ranks, parallel to the
two players' "sides" of the board.

DIAGRAM 3-2: WAVY RANKS
=======================
______
/\ 7  /\
/ 7  \/  7 \
/\    /  \    /\
/_7__\/      \/__7_\
|    |        |    |
|____|        |____|
/\ 5  /\      /\ 5  /\
/ 5  \/ 5  \  / 5  \/ 5  \
/\    /  \    /\    /  \    /\
/_5__\/      \/_5__\/      \/_5__\
|    |        |    |        |    |
|____|        |____|        |____|
\ 3  /\      /\ 3  /\      /\  3 /
\/    \  /    \/    \  /    \/
\ 3  /\ 3  /  \ 3  /\  3 /
\/_3__\/      \/_3__\/
|    |        |    |
|____|        |____|
\ 1  /\      /\  1 /
\/    \  /    \/
\ 1  /\  1 /
\/_1__\/

In Diagram 3-2 above, four horizontal rows of cells have been
marked: the first ("111"), third ("333"), fifth ("555"), and seventh
("777").  These are "wavy ranks."

DIAGRAM 3-3: Y-AXIS FILES
=========================
______
/\ e  /\
/    \/    \
/\    /  \    /\
/_c__\/      \/__g_\
| c  |   e    |  g |
|____|        |____|
/\ c  /\      /\  g /\
/    \/    \  /    \/    \
/\    /  \    /\    /  \    /\
/_a__\/      \/_e__\/      \/__i_\
| a  |   c    | e  |    g   |  i |
|____|        |____|        |____|
\ a  /\      /\ e  /\      /\  i /
\/    \  /    \/    \  /    \/
\    /\    /  \    /\    /
\/_c__\/      \/__g_\/
| c  |   e    |  g |
|____|        |____|
\ c  /\      /\  g /
\/    \  /    \/
\    /\    /
\/_e__\/

In Diagram 3-3 above, five vertical lines of connected cells
("files") have been marked.  These files are: 'a' ("aaa"), 'c'
("ccc"), 'e' ("eee"), 'g' ("ggg"), and 'i' ("iii").  These are true
Y-axis files, which can be viewed as straight lines connecting the
two players, or as perpendicular to the X-axis ranks.

DIAGRAM 3-4: OTHER FILES FOR NOTATION
=====================================
______
/\    /\
/ d  \/  f \
/\    /  \    /\
/____\/      \/____\
|    |        |    |
|____|        |____|
/\    /\      /\    /\
/ b  \/  d \  / f  \/  h \
/\    /  \    /\    /  \    /\
/____\/      \/____\/      \/____\
|    |        |    |        |    |
|____|        |____|        |____|
\    /\      /\    /\      /\    /
\/    \  /    \/    \  /    \/
\ b  /\  d /  \ f  /\  h /
\/____\/      \/____\/
|    |        |    |
|____|        |____|
\    /\      /\    /
\/    \  /    \/
\ d  /\  f /
\/____\/

In Diagram 3-4 above, the cells that are not part of Y-axis files
have been grouped into four vertical lines.  These lines of discon-
nected or noncontiguous cells are being noted solely for the purpose
of notation.  These marked files are: 'b' ("bbb"), 'd' ("ddd"), 'f'
("fff"), and 'h' ("hhh").

3.5  ALGEBRAIC NOTATION
=======================

As in Regular Chess, each cell is denoted by two coordinates.  The
first is the letter of the file; the second is the number of the rank.
The board is numbered starting from the left end of White's side.
Ranks are numbered 1 to 7 from White's side to Black's side.  Files
are lettered 'a' to 'i' from White's left to right.  In diagrams
White's side is pictured at the bottom; White moves up the diagram.
Black's side is pictured at the top; Black moves down the diagram.

Chessplayers should bear in mind that identification of the odd-
numbered, wavy ranks and of the even-lettered, noncontiguous files as
discrete entities in the above diagrams is done solely for the purpose
of denoting cells on the board for algebraic notation.  Pieces could
be invented and defined as limited to moving along such lines, of
course, but at the present time no such pieces are being suggested for
the 39-cell board.

DIAGRAM 3-6: THE ENTIRE BOARD
=============================
______
/\ e7 /\
7              / d7 \/ f7 \
/\    /  \    /\
/_c7_\/      \/_g7_\
6          | c6 |   e6   | g6 |
|____|        |____|
/\ c5 /\      /\ g5 /\
5       / b5 \/ d5 \  / f5 \/ h5 \
/\    /  \    /\    /  \    /\
/_a5_\/      \/_e5_\/      \/_i5_\
4   | a4 |   c4   | e4 |   g4   | i4 |
|____|        |____|        |____|
\ a3 /\      /\ e3 /\      /\ i3 /
3     \/    \  /    \/    \  /    \/
\ b3 /\ d3 /  \ f3 /\ h3 /
\/_c3_\/      \/_g3_\/
2          | c2 |   e2   | g2 |
|____|        |____|
\ c1 /\      /\ g1 /
\/    \  /    \/
1              \ d1 /\ f1 /
\/_e1_\/

a   b  c  d   e   f  g  h   i

Diagram 3.6 above shows the completed board.  For notation there
are seven ranks and nine files.  Ranks '2' and '6' have 3 cells;
ranks '1', '4', and '7' have 5 cells; ranks '3' and '5' have 9 cells.
Files 'b' and 'h' have 2 cells; files 'a' and 'i' have 3 cells; files
'd' and 'f' have 4 cells; files 'c', 'e', and 'g' consist of 7 cells.

An easy way to remember the notation system is to note that the
central rank is the fourth rank, and the central file is the 'e'
file.

4.0  CONSTRUCTING AN ACTUAL BOARD
=================================

For a desk-sized or analysis set (2 1/2-inch King), triangles and
squares should have sides of 1 3/4 to 2 inches; for a full-sized tour-
nament set, 2 1/4 to 2 1/2 inches.  For proper proportions, triangles
and hexagons are regular (60-degree angles).

DIAGRAM 4-1: TRIANGLES
======================
______
/\ x  /\
/    \/    \
/\    /  \    /\
/_o__\/      \/__o_\
|    |        |    |
|____|        |____|
/\ o  /\      /\  o /\
/    \/    \  /    \/    \
/\    /  \    /\    /  \    /\
/_x__\/      \/_x__\/      \/_x__\
|    |        |    |        |    |
|____|        |____|        |____|
\ x  /\      /\ x  /\      /\ x  /
\/    \  /    \/    \  /    \/
\    /\    /  \    /\    /
\/_o__\/      \/__o_\/
|    |        |    |
|____|        |____|
\ o  /\      /\  o /
\/    \  /    \/
\    /\    /
\/_x__\/

The color scheme given here is suggested mainly for visual con-
venience when using notation.  However, this color scheme is also
useful for identifying certain patterns described later in this
article.  Triangles marked "x" are colored solid red; those marked "o"
are outlined in red around their inner border (in effect leaving a
white triangle within a red triangle).  Hexagons are left uncolored
(white or buff).

DIAGRAM 4-2: SQUARES
====================
______
/\    /\
/ o  \/  o \
/\    /  \    /\
/____\/      \/____\
| x  |        |  x |
|____|        |____|
/\    /\      /\    /\
/ \$  \/  o \  / o  \/  \$ \
/\    /  \    /\    /  \    /\
/____\/      \/____\/      \/____\
| x  |        | x  |        |  x |
|____|        |____|        |____|
\    /\      /\    /\      /\    /
\/    \  /    \/    \  /    \/
\ \$  /\  o /  \ o  /\  \$ /
\/____\/      \/____\/
| x  |        |  x |
|____|        |____|
\    /\      /\    /
\/    \  /    \/
\ o  /\  o /
\/____\/

Squares marked "x" are colored solid blue.  Those marked "\$" are
outlined in blue around their inner border (in effect leaving a white
square within a blue square).  Those marked "o" are zebra-striped with
blue lines.

CHAPTER :III:  VECTORS
======================

5.0  VECTORS: THE FOUR AXES
===========================

There are six axes on the lotus board that denote directions of
possible movement along lines of cells.  These axes are identified by
straight lines connecting the centers of contiguous cells.  This
article will describe and illustrate only those types of lines meet-
ing this standard, or used by pieces mentioned in the accompanying
article, CHESS PIECES IN THE LOTUS ENVIRONMENT.  Additional types of
lines of cells, which might be described with nonstraight lines, or
which might consist of noncontiguous cells, or which might be defined
in other ways, will be left for future articles.

For practical use, the six axes can be reduced to four types: the
X-axis, the Y-axis, the two Z-axes, and the two W-axes.

5.1  THE X-AXIS
===============

The X-axis has already been illustrated in Diagram 3-1.  The three
even-numbered ranks are the only true X-axis lines on the board.  An
X-axis line, by definition, must be exactly parallel to the two play-
ers' sides of the board (i.e., the "back rank" on a regular 8x8
board).  Strictly speaking, the term "X-axis" without additional qual-
ifiers should not be used for wavy rows like the third or fifth ranks.
For another example, a line of cells like c2-g2 (or c2-e2-g2) is not a
true X-axis line.  Also, note that the ASCII diagram is misleading in
appearance; the cells b5-d5-f5-g5 are not a true X-axis line.

5.2  THE Y-AXIS
===============

The Y-axis has already been illustrated in Diagram 3-3.  The five
odd-lettered files are the only true Y-axis lines on the board.  A
Y-axis line, by definition, must be exactly perpendicular to the
X-axis.  In other words, the Y-axis is perpendicular to the two play-
ers' "sides" of the board.  Strictly speaking, the term "Y-axis" with-
out additional qualifiers should not be used for wavy rows (i.e.,
lotus paths) that snake across the board from one player's side to the
other.  Nor should it be used for paths like the series of zebra-
striped blue squares and intermediate hexagons like the path f7-e6-f5-
g4-f3-e2-f1, or the shorter b5-c4-b3.  Those are not true Y-axis
lines.

DIAGRAM 5-3: THE Z-AXES (1)
===========================
______
/\    /\
7              /*    \/   \
/\  * /  \    /\
/____\/      \/_x__\
6          |    |  *     | x  |
|____|   *    |____|
/\    /\    * /\ x  /\
5       / *  \/    \  / x  \/    \
/\   */  \    /\  * /  \    /\
/____\/ *    \/_x__\/ *    \/____\
4   |    |   *    | x  |   *    |    |
|____|    *   |____|    *   |____|
\    /\    * /\ x  /\    * /\    /
3     \/    \  / x  \/    \  /*   \/
\    /\  * /  \    /\  * /
\/_x__\/*     \/____\/
2          |    |  *     |    |
|____|   *    |____|
\    /\   *  /\    /
\/    \  /    \/
1              \    /\  * /
\/____\/

a   b  c  d   e   f  g  h   i

In Diagram 5-3 above, the two northwest-to-southeast Z-axes are
marked with asterisks ("***").  See Diagram 5-4 for the other two
Z-axes.  The wavy line of contiguous cells running from h7 to c2
(marked "xxx") is not a straight line and thus does not qualify to be
referred to as a true Z-axis line.

DIAGRAM 5-4: THE Z-AXES (2)
===========================
______
/\    /\
7              /     \/  % \
/\    /  \    /\
/____\/   %  \/____\
6          |    |   %    |    |
|____|  %     |____|
/\    /\      /\    /\
5       /    \/ %  \  /    \/  % \
/\    /  \    /\    /  \    /\
/____\/   %  \/____\/   %  \/____\
4   |    |   %    |    |   %    |    |
|____|  %     |____|  %     |____|
\    /\      /\    /\      /\    /
3     \/ %  \  /    \/ %  \  /    \/
\    /\    /  \    /\    /
\/____\/   %  \/____\/
2          |    |   %    |    |
|____|  %     |____|
\    /\      /\    /
\/ %  \  /    \/
1              \    /\    /
\/____\/

a   b  c  d   e   f  g  h   i

In Diagram 5-4 above, the two northeast-to-southwest Z-axes are
marked with percent signs ("%%%").  See Diagram 5-3 for the other two
Z-axes.  All of these four Z-axes are true orthogonal rows (as are the
even-numbered, X-axis ranks).

Z-axis lines may sometimes be referred to as files, or as Z-files.
This usage has validity as convenient shorthand terminology since
these Z-axis rows are the only true orthogonal rows connecting the two
players' sides of the board.  Notice that these Z-files, in running
between each player's third rank and the back rank of the opponent,
are equal in length (i.e., five cells) as a path for "vertical" move-
ment to the true Y-axis files.  (The W-axis lines described in the
next section don't match these same descriptions, which is why they're
not called files!)

DIAGRAM 5-5: THE V-AXIS
=======================
______
/\  * /\
/    \/ *  \
/\    /  \  * /\
/__%_\/      \/_*__\
|    |  %     |    |
|____|     %  |____|
/\    /\      /\ %  /\
/    \/    \  /    \/ %  \
/\    /  \    /\    /  \  % /\
/____\/      \/____\/      \/__%_\
|    |        |    |        |    |
|____|        |____|        |____|
\ \$  /\      /\    /\      /\    /
\/ \$  \  /    \/    \  /    \/
\  \$ /\    /  \    /\    /
\/__\$_\/      \/____\/
|    |  \$     |    |
|____|     \$  |____|
\    /\      /\ \$  /
\/    \  /    \/
\    /\    /
\/____\/

Diagram 5-5 above illustrates three of the V-axis lines ("***,"
"%%%," "\$\$\$") which are parallel to each other in the northwest to
southeast direction.  These are not the only V-axis lines; there are
others that aren't marked.  In ordinary practice, V-axis and W-axis
lines are both referred to by the name "W-axis."  See also Section
5-6 below.

DIAGRAM 5-6: THE W-AXIS
=======================
______
/\    /\
/    \/    \
/\    /  \    /\
/____\/      \/_@__\
|    |     @  |    |
|____|  @     |____|
/\  @ /\      /\    /\
/  @ \/    \  /    \/    \
/\ @  /  \    /\    /  \    /\
/_@__\/      \/____\/      \/____\
|    |        |    |        |    |
|____|        |____|        |____|
\    /\      /\    /\      /\ #  /
\/    \  /    \/    \  /  # \/
\    /\    /  \    /\ #  /
\/____\/      \/_#__\/
|    |      # |    |
|____|  #     |____|
\ #  /\      /\ x  /
\/    \  /  x \/
\    /\ x  /
\/_x__\/

Diagram 5-6 above illustrates three of the W-axis lines ("@@@,"
"###," "xxx") which are parallel to each other in the southwest to
northeast direction.  These are not the only W-axis lines; there are
others that aren't marked.  In ordinary practice, reference to the
"W-axis" connotes both W-axis lines and V-axis lines.  See also Sec-
tion 5-5 above.

The W-axis (and V-axis) lines are straight paths connecting the
centers of contiguous cells where every other cell is a triangle.
Since a line drawn to represent these axes goes thru the pointy cor-
ners of the triangles and hexagons, W-axis paths are not orthogonal.
(See Section 6.0 below.)

6.0  ORTHOGONALITY
==================

A.S.M. Dickins defined "orthogonal" as movement along a rank or
file.  This definition needs to be tightened up when applied to other
shapes and configurations.  An orthogonal line or path can be defined
as consisting of a series of connected (contiguous) cells thru all of
which a straight line can be drawn, and where the sides of all such
cells which that line intersects are perpendicular to that line.
Any other sides of those cells -- i.e., sides not intersected by the
drawn line -- are irrelevant.

On the lotus board, the three even-numbered X-axis ranks and the
four Z-axis files meet this standard, since all sides intersected by
the line connecting the centers of the contiguous cells are perpen-
dicular to that line.  The hexagons' additional, nonintersected sides
have no bearing on the matter.  The W-axis lines do not meet the stan-
dard since the straight line that connects them extends thru the
pointy ends of triangular and hexagonal cells; those intersected sides
of those cells are not at a 90-degree angle to the line drawn along
the W-axis, therefore the W-axes are not orthogonal.

A question arises as to whether this definition allows for a cell
like a triangle to be on the end of an orthogonal row.  It might be
said that a line drawn to represent the orthogonal row can stop in the
middle of the cell on each end; as long as all the cells in between
meet the definition of orthogonalness, there's no need to extend the
imaginary line past the end of the row of cells.  By this standard the
'a' and 'i' files on the 39-cell lotus board could be called orthogo-
nal, and lines like e7-f7-g7 or e1-f1-g1 might be raised to a sort of
"rank" status as a result.  This author considers such reasoning a
slippery slope which seems to lead to no good, and therefore rejects
it.  Defining orthogonality too liberally would make problems in de-
fining the move of the Rook, for example.  It's probably best to in-
sist that the end-sides of the end-cells of an orthogonal line also be
perpendicular to that line, which rules out triangles being end-cells.
See discussion of superorthogonality in Section 6.1 below.

6.1  SUPERORTHOGONALITY
=======================

The lotus board motivates the delineation of a new concept: the
superorthogonal line of cells.  A superorthogonal path consists of
a series of connected (contiguous) cells along a true X-axis or true
Y-axis line.  Superorthogonal ("superortho" for short) lines include
the intermediate and end-border cells.

On the 39-cell lotus board, there are eight superorthogonal paths:
*  the 2nd, 4th, and 6th ranks on the X-axis.  Cells that are
on these lines are illustrated in Diagram 3-1.
and *  the a - c - e - g - i files on the Y-axis.  Cells that are
on these lines are illustrated in Diagram 3-3.

CHAPTER :IV:  PATTERNS
======================

7.0  ROWS (AND RANKS)
=====================

There are two types of rows: orthogonal and non-orthogonal.  Some
orthogonal rows are ranks; others are files.  The orthogonal rows are:
(1) the 2nd, 4th, and 6th ranks on the X-axis.  See Diagram
3-1.
and (2) the four Z-files on the Z-axes.  See Diagrams 5-3 and 5-4.

The non-orthogonal rows are the lotus or wavy rows.  Examples are
the 1st, 3rd, 5th, and 7th ranks.  See Diagram 3-2.

"Rank" is mainly a notational term.  There are two types of ranks:
orthogonal and wavy.  See Sections 3.1 and 3.2.

7.1  FILES
==========

There are three types of files:
(1) Superorthogonal files: a - c - e - g - i.  In all, five
files on the Y-axis.  See Diagram 3-3.
(2) The Z-files.  Four files in all, on the Z-axes.  See
Diagrams 5-3 and 5-4.
(3) The hypothecated lines of the b - d - f - h files.  See
Diagram 3-4.

7.2  DIAGONALS
==============

In all, there are 17 diagonals on the 39-cell lotus board.  They
are of three types:
(1) Six lines of cells along the V-axis.  See Diagram 5-5.
(2) Six lines of cells along the W-axis.  See Diagram 5-6.
(3) The five superorthogonal files: a - c - e - g - i.  See
Diagram 3-3.  These lines are the same as the W-axes lines except that
they're oriented along the Y-axis.

Diagonals may be said to consist of these entire lines, including
intermediate cells (squares and hexagons), or they may be defined as
consisting only of certain cells (such as the triangles) along these
lines.  It depends on the piece being considered.  Generally speaking,
the term "diagonal" is synonymous with these entire lines.  However,
when a piece such as the Alfil or Alfilrider is referred to, it's un-
derstood that such a piece moves only on the triangles of the diago-
nals, and not on the intermediate non-triangular cells.

8.0  LOTUS PATHS
================

The special feature of the lotus board is the continuous row of
cells that snakes around the board along the path of the lotus petals.

DIAGRAM 8-1: LOTUS PATH MOVEMENT
================================
______
/\    /\
/ x  \/    \
/\ x  /  \    /\
/__x_\/      \/____\
| x  |        |    |
|_x__|        |____|
/\ x  /\      /\ x  /\
/  x \/    \  /  x \/ x  \
/\ x  /  \    /\ x  /  \  x /\
/__x_\/      \/__x_\/      \/____\
| x  |        | x  |        |    |
|_x__|        |_x__|        |____|
\  x /\      /\ x  /\      /\    /
\/ x  \  /  x \/    \  /    \/
\  x /\ x  /  \    /\    /
\/_x__\/      \/____\/
|    |        |    |
|____|        |____|
\    /\      /\    /
\/    \  /    \/
\    /\    /
\/____\/

Diagram 8-1 above displays a possible lotus-path movement ("xxx").
A Lotus-rider could start at 'd7' and swirl around the board until
stopping on 'h5'.  This is only a sample of lotus movement.  There are
many possible lotus-path moves.  All four lotus petals constitute one
continuous pathway, consisting of contiguous wavy rows of triangles
and squares.  Some triangles are branching points for moving from one
lotus petal to another.  Hexagons are not part of the lotus rows.

DIAGRAM 8-2: LOTUS CIRCLES
==========================
______
/\    /\
/    \/    \
/\    /  \    /\
/____\/      \/____\
|    |        |    |
|____|        |____|
/\    /\      /\ x  /\
/    \/    \  / x  \/ x  \
/\    /  \    /\x   /  \  x /\
/____\/      \/_x__\/      \/_x__\
|    |        | x  |        |  x |
|____|        |_x__|        |__x_|
\    /\      /\  x /\      /\ x  /
\/    \  /    \/ x  \  /  x \/
\    /\    /  \  x /\ x  /
\/____\/      \/_x__\/
|    |        |    |
|____|        |____|
\    /\      /\    /
\/    \  /    \/
\    /\    /
\/____\/

Diagram 8-2 above illustrates one of the four possible lotus cir-
cles.  Each lotus petal may be considered a separate circle, or all
four may be considered as linked, depending on the piece being used
and how its movement is defined.  See also Section 8-1.  Hexagons are
not part of the lotus circle.

8.3  OTHER LOTUS PATTERNS
=========================

The half-lotus is a pattern of cells in a lotus circle consisting
of only the squares, or alternately, of only the triangles.  (Compare
with Diagram 8-2 above.)

9.0  OTHER PATTERNS
===================

See Section 5.0 about concepts of patterns not mentioned in this
article.

9.1  TRIANGLES
==============

The 16 triangles as a group constitute 41% of the cells on the
board.  See Section 7.2 for discussion of the role of the triangle
cells in diagonals.  The triangle cells are components of the W-axes
and Y-axis lines; there are no triangles in the true orthogonal lines
of the X-axis ranks or Z-axis files.  The triangles are non-contigu-
ous.

9.2  SQUARES
============

The 19 squares as a group constitute 49% of the cells on the board.
Note that whereas the triangles and hexagons are non-contiguous, the
squares are connected to each other at their corners.  Every square
touches at least two other squares; some touch three or four other
squares.

9.3  HEXAGONS
=============

The four hexagons as a group constitute 10% of the cells on the
board.  The pattern of cells composed of the four hexagons by them-
selves is called a hexie.  The four hexagons, sometimes abbreviated
to "hexes," are non-contiguous.

[Version 1.2: published November 30, 1998.]

```

A hardcopy printout of the four main files dealing with Lotus Chess is available from the author for US \$14.95 (includes shipping cost to U.S. addresses only). "Lotus Chess: The Book" is spiral-bound and also contains a full-sized, full-color board for use in playing the game. For address information, contact inventor David Moeser by e-mail at: erasmus at iglou dot com.
Written by David Moeser (c).
This is part of a submission to the contest to design a chess variant on a board with 39 squares.
WWW page created: December 7, 1998. Last modified: June 1, 1999. ﻿