## assoc-list/l-for-lookup [ Classes ]

[ Top ] [ assoc-list ] [ Classes ]

NAME

l-for-lookupFile:l-for-lookupClass Hierarchy: named-object -> linked-named-object -> sclist -> circular-sclist -> assoc-list ->l-for-lookupVersion: 1.0.12 Project: slippery chicken (algorithmic composition) Purpose: Implementation of thel-for-lookupclass. The name stands for L-System for Lookups (L for Lindenmayer). This provides an L-System function for generating sequences of numbers from rules and seeds, and then using these numbers for lookups into the assoc-list. In the assoc list are stored groups of numbers, meant to represent in the first place, for example, rhythmic sequences. The grouping could be as follows: ((2 3 7) (11 12 16) (24 27 29) and would mean that a transition should take place (over the length of the number of calls represented by the number of L-Sequence results) from the first group to the second, then from the second to the third. When the first group is in use, then we will simple cycle around the given values, similar with the other groups. The transition is based on a fibonacci algorithm (see below). The sequences are stored in the data slot. The l-sequence will be a list like (3 1 1 2 1 2 2 3 1 2 2 3 2 3 3 1). These are the references into the assoc-list (the 1, 2, 3 ids in the list below). e.g. ((1 ((2 3 7) (11 16 12))) (2 ((4 5 9) (13 14 17))) (3 ((1 6 8) (15 18 19)))) Author: Michael Edwards: m@michael-edwards.org Creation date: 15th February 2002 $$ Last modified: 16:20:46 Fri Apr 23 2021 CEST SVN ID: $Id$

## l-for-lookup/count-elements [ Functions ]

[ Top ] [ l-for-lookup ] [ Functions ]

DESCRIPTION

Count the number of times each element occurs in a given list.

ARGUMENTS

- A list of numbers or symbols (or anything which can be compared using EQL).

RETURN VALUE

Returns a list of two-element lists, each consisting of one list element from the specified list and the number of times that element occurs in the list. If the elements are numbers, these will be sorted from low to high, otherwise symbols will be returned from most populous to least.

EXAMPLE

(count-elements'(1 4 5 7 3 4 1 5 4 8 5 7 3 2 3 6 3 4 5 4 1 4 8 5 7 3 2)) => ((1 3) (2 2) (3 5) (4 6) (5 5) (6 1) (7 3) (8 2))

SYNOPSIS

(defuncount-elements(list)

## l-for-lookup/do-lookup [ Methods ]

[ Top ] [ l-for-lookup ] [ Methods ]

DESCRIPTION

Generate an L-sequence from the rules of the specified l-for-lookup object and use it to perform the Fibonacci-based transitioning look-up of values in the specified sequences. NB As this accesses the rules as circular lists whose states are not reset before starting, you may get (desired) different results if you call the routine more than once. In order to avoid that call (reset lflu) beforedo-lookup.

ARGUMENTS

- An l-for-lookup object. - The start seed, or axiom, that is the initial state of the L-system. This must be the key-id of one of the sequences. - An integer that is the length of the sequence to be returned. NB: This number does not indicate the number of L-system passes, but only the number of elements in the list returned, which may be the first segment of a sequence returned by a pass that actually generates a much longer sequence.

OPTIONAL ARGUMENTS

- A number which is the factor by which returned numerical values are to be scaled. If NIL, the method will use the value in the given l-for-lookup object's SCALER slot instead. Default = NIL. NB: The value of the given l-for-lookup object's OFFSET slot is additionally used to increase numerical values before they are returned.

RETURN VALUE

This method returns three lists: - The resulting sequence. - The distribution of the values returned by the look-up. - The L-sequence of the key-IDs.

EXAMPLE

;; Create an l-for-lookup object in which the sequences are defined such that ;; the transition takes place over the 3 given lists and from x to y to z, and ;; apply thedo-lookupmethod to see the results. Each time one of these lists ;; is accessed, it will cyclically return the next value. (let ((lfl (make-l-for-lookup 'lfl-test '((1 ((ax1 ax2 ax3) (ay1 ay2 ay3 ay4) (az1 az2 az3 az4 az5))) (2 ((bx1 bx2 bx3) (by1 by2 by3 by4) (bz1 bz2 bz3 bz4 bz5))) (3 ((cx1 cx2 cx3) (cy2 cy2 cy3 cy4) (cz1 cz2 cz3 cz4 cz5)))) '((1 (1 2 2 2 1 1)) (2 (2 1 2 3 2)) (3 (2 3 2 2 2 3 3)))))) (do-lookuplfl 1 211)) => (AX1 BX1 BX2 BX3 AX2 AX3 BX1 AX1 BX2 CX1 BX3 BX1 AX2 BX2 CX2 BX3 BX1 AX3 BX2 CX3 BX3 AX1 BY1 BX1 BX2 AY1 AX2 AX3 BX3 BX1 BX2 AX1 AX2 BX3 AY2 BX1 CX1 BY2 AX3 BX2 BX3 BX1 AX1 AY3 BX2 AX2 BY3 CY2 BX3 BX1 CX2 BY4 BX2 BX3 CX3 CY2 BY1 AY4 BX1 CX1 BY2 BX2 AY1 BY3 CY3 BY4 AX3 BX3 BY1 BX1 AY2 AX1 BY2 AY3 BY3 CY4 BX2 BY4 CX2 BY1 BX3 BY2 CY2 CX3 BY3 AY4 BY4 CY2 BY1 BX1 AX2 BY2 CY3 BY3 AY1 BY4 BY1 BY2 AY2 AY3 BY3 AY4 BY4 CY4 BY1 BY2 CY2 BY3 BY4 BY1 CY2 CY3 BY2 AY1 BY3 CY4 BY4 AY2 BY1 BY2 BY3 AY3 AY4 BY4 AY1 BY1 CZ1 BZ1 BY2 AY2 BY3 CY2 BY4 BY1 AY3 BY2 CY2 BY3 AY4 BY4 BZ2 BY1 AZ1 AY1 AY2 BY2 BY3 BY4 AY3 AY4 AZ2 BZ3 BY1 BY2 AY1 AY2 BZ4 AZ3 BY3 CZ2 BY4 BZ5 AY3 BY1 CY3 BZ1 BY2 AZ4 BZ2 CZ3 BZ3 AZ5 BY3 BZ4 BY4 AY4 AZ1 AY1 BZ5 BZ1 BY1 AZ2 AZ3 BZ2 AY2 BZ3 CY4 BY2 AZ4 BZ4 BZ5 BZ1 AZ5 AZ1 BZ2 AZ2 BY3 CZ4 BZ3 BZ4 CY2 BZ5 BZ1 BZ2 CZ5 CZ1 BZ3 AZ3 BZ4 CZ2 BZ5), ((CX1 3) (AX3 5) (AX1 6) (BX2 11) (CX2 3) (BX3 11) (CX3 3) (BX1 12) (AX2 6) (AY3 7) (CY3 4) (CZ3 1) (BY4 14) (AY4 7) (AY1 8) (BY1 15) (AY2 8) (CY4 4) (BY2 15) (AZ4 2) (AZ5 2) (AZ1 3) (AZ2 3) (BY3 15) (CZ4 1) (CY2 9) (BZ1 5) (BZ25) (CZ5 1) (CZ1 2) (BZ3 5) (AZ3 3) (BZ4 5) (CZ2 2) (BZ5 5)), (1 2 2 2 1 1 2 1 2 3 2 2 1 2 3 2 2 1 2 3 2 1 2 2 2 1 1 1 2 2 2 1 1 2 1 2 3 2 1 2 2 2 1 1 2 1 2 3 2 2 3 2 2 2 3 3 2 1 2 3 2 2 1 2 3 2 1 2 2 2 1 1 2 1 2 3 2 2 3 2 2 2 3 3 2 1 2 3 2 2 1 2 3 2 1 2 2 2 1 1 2 1 2 3 2 2 3 2 2 2 3 3 2 1 2 3 2 1 2 2 2 1 1 2 1 2 3 2 2 1 2 3 2 2 1 2 3 2 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 2 1 2 3 2 2 1 2 3 2 2 1 2 3 2 1 2 2 2 1 1 1 2 2 2 1 1 2 1 2 3 2 1 2 2 2 1 1 2 1 2 3 2 2 3 2 2 2 3 3 2 1 2 3 2)

SYNOPSIS

(defmethoddo-lookup((lflu l-for-lookup) seed stop &optional scaler)

## l-for-lookup/do-lookup-linear [ Methods ]

[ Top ] [ l-for-lookup ] [ Methods ]

DESCRIPTION

Similar to do-lookup but here we generate a linear sequence (with get-linear-sequence) instead of an L-System.

ARGUMENTS

- An l-for-lookup object. - The start seed, or axiom, that is the initial state of the linear system. This must be the key-id of one of the sequences. - An integer that is the length of the sequence to be returned.

OPTIONAL ARGUMENTS

keyword arguments: - :scaler. A number which is the factor by which returned numerical values are to be scaled. If NIL, the method will use the value in the given l-for-lookup object's SCALER slot instead. Default = NIL. NB: The value of the given l-for-lookup object's OFFSET slot is additionally used to increase numerical values before they are returned. Default = NIL. - :reset. T or NIL to indicate whether to reset the pointers of the given circular lists before proceeding. T = reset. Default = T.

RETURN VALUE

This method returns three lists: - The resulting sequence. - The distribution of the values returned by the look-up. - The L-sequence of the key-IDs.

EXAMPLE

;; This will return the result of lookup, the number of repetitions of each ;; rule key in the result of lookup, and the linear-sequence itself. (let* ((tune (make-l-for-lookup 'tune '((1 ((2 1 8))) (2 ((3 4))) (3 ((4 5))) (4 ((5 1 6))) (5 ((6 5 7 4))) (6 ((4 5))) (7 ((4 5 1))) (8 ((1)))) '((1 (1 2)) (2 (1 3 2)) (3 (1 4 3)) (4 (1 2 1)) (5 (5 3 1)) (6 (2 5 6)) (7 (5 6 4)) (8 (3 2)))))) (do-lookup-lineartune 1 100)) => (2 1 3 8 2 4 4 1 8 3 4 2 1 3 5 5 8 2 4 3 1 8 4 4 5 2 1 3 4 8 2 3 4 1 4 3 1 8 4 5 4 2 1 3 4 8 2 3 5 6 1 8 4 3 2 1 4 4 5 8 2 3 4 1 8 3 4 5 2 1 4 3 8 2 4 5 4 1 8 3 4 2 1 3 5 1 4 3 8 2 4 4 5 1 8 3 4 2 1 3) ((1 17) (2 15) (3 18) (4 25) (5 10) (6 1) (8 14)) (1 1 2 1 1 2 3 1 1 2 2 1 1 2 3 4 1 1 2 2 1 1 2 3 3 1 1 2 2 1 1 2 3 4 2 2 1 1 2 3 3 1 1 2 2 1 1 2 3 4 1 1 2 2 1 1 2 3 3 1 1 2 2 1 1 2 3 4 1 1 2 2 1 1 2 3 3 1 1 2 2 1 1 2 3 4 2 2 1 1 2 3 3 1 1 2 2 1 1 2)

SYNOPSIS

(defmethoddo-lookup-linear((lflu l-for-lookup) seed stop &key scaler (reset t))

## l-for-lookup/do-simple-lookup [ Methods ]

[ Top ] [ l-for-lookup ] [ Methods ]

DESCRIPTION

Performs a simple look-up procedure whereby a given reference key always returns a specific and single piece of data. This is different from do-lookup, which performs a transitioning between lists and returns items from those lists in a circular manner.do-simple-lookupalways returns the first element of the sequence list associated with a given key-ID. N.B. the SCALER and OFFSET slots are ignored by this method.

ARGUMENTS

- An l-for-lookup object. - The start seed, or axiom, that is the initial state of the L-system. This must be the key-id of one of the sequences. - An integer that is the number of elements to be returned.

RETURN VALUE

EXAMPLE

;; Create an l-for-lookup object using three production rules and three ;; sequences of three lists. Applyingdo-simple-lookupreturns the first ;; element of each sequence based on the L-sequence of keys created by the ;; rules of the give l-for-lookup object. (let ((lfl (make-l-for-lookup 'lfl-test '((1 ((ax1 ax2 ax3) (ay1 ay2 ay3 ay4) (az1 az2 az3 az4 az5))) (2 ((bx1 bx2 bx3) (by1 by2 by3 by4) (bz1 bz2 bz3 bz4 bz5))) (3 ((cx1 cx2 cx3) (cy2 cy2 cy3 cy4) (cz1 cz2 cz3 cz4 cz5)))) '((1 (1 2 2 2 1 1)) (2 (2 1 2 3 2)) (3 (2 3 2 2 2 3 3)))))) (do-simple-lookuplfl 1 21)) => ((AX1 AX2 AX3) (BX1 BX2 BX3) (BX1 BX2 BX3) (BX1 BX2 BX3) (AX1 AX2 AX3) (AX1 AX2 AX3) (BX1 BX2 BX3) (AX1 AX2 AX3) (BX1 BX2 BX3) (CX1 CX2 CX3) (BX1 BX2 BX3) (BX1 BX2 BX3) (AX1 AX2 AX3) (BX1 BX2 BX3) (CX1 CX2 CX3) (BX1 BX2 BX3) (BX1 BX2 BX3) (AX1 AX2 AX3) (BX1 BX2 BX3) (CX1 CX2 CX3) (BX1 BX2 BX3))

SYNOPSIS

(defmethoddo-simple-lookup((lflu l-for-lookup) seed stop)

## l-for-lookup/fibonacci [ Functions ]

[ Top ] [ l-for-lookup ] [ Functions ]

DESCRIPTION

Return the longest possible list of sequential Fibonacci numbers whose combined sum is less than or equal to the specified value. The list is returned in descending sequential order, ending with 0. The function also returns as a second individual value the first Fibonacci number that is greater than the sum of the list returned. NB: The value of the second number returned will always be equal to the sum of the list plus one. In most cases that number will be less than the number specified as the argument to thefibonaccifunction, and sometimes it will be equal to the number specified; but in cases where the sum of the list returned is equal to the number specified, the second number returned will be equal to the specified number plus one.

ARGUMENTS

A number that is to be the test number.

RETURN VALUE

A list of descending sequential Fibonacci numbers, of which list the last element is 0. Also returns as a second individual value the first Fibonacci number that is greater than the sum of the list returned, which will always be the sum of that list plus one.

EXAMPLE

;; Returns a list of consecutive Fibonacci numbers from 0 whose sum is equal to ;; or less than the value specified. The second number returned is the first ;; Fibonacci number whose value is greater than the sum of the list, and will ;; always be the sum of the list plus one. (fibonacci5000) => (1597 987 610 377 233 144 89 55 34 21 13 8 5 3 2 1 1 0), 4181 ;; The sum of the list (+ 1597 987 610 377 233 144 89 55 34 21 13 8 5 3 2 1 1 0) => 4180

SYNOPSIS

(defunfibonacci(max-sum)

## l-for-lookup/fibonacci-divide [ Functions ]

[ Top ] [ l-for-lookup ] [ Functions ]

DATE

August 5th 2019, Heidhausen

DESCRIPTION

Divide an integer into ever smaller proportions as determined by a Fibonacci series which sums to the largest Fibonacci number less than the given integer. The resulting list is of ascending (accumulating) numbers which are scaled to fit the given integer (optionally but by default) and (optionally but also by default) rounded. As such, this routine is useful for determining, for examples, bar numbers at which events/changes might happen.

ARGUMENTS

- an integer

OPTIONAL ARGUMENTS

- T or NIL: whether to scale the Fibonacci numbers to fit the given integer. Default = T. - T or NIL: whether to round after scaling

RETURN VALUE

A list of numbers

EXAMPLE

(FIBONACCI-DIVIDE 300) --> (116 187 230 258 274 285 291 295 297 299 300) ;;; don't scale to 300 (i.e. only increase by Fibonacci numbers but note that ;;; the Fibonacci number is added to the current number, which starts at one, ;;; hence 1+89, 90+55, 145+34 ... (FIBONACCI-DIVIDE 300 nil) --> (90 145 179 200 213 221 226 229 231 232 233) ;;; do scale but don't round (FIBONACCI-DIVIDE 300 t nil) --> (115.87983 186.69528 230.4721 257.51074 274.24893 284.54935 290.98712 294.8498 297.4249 298.71246 300.0)

SYNOPSIS

(defunfibonacci-divide(num &optional (scale t) (round t))

## l-for-lookup/fibonacci-start-at-2 [ Functions ]

[ Top ] [ l-for-lookup ] [ Functions ]

DESCRIPTION

Return the longest possible list of sequential Fibonacci numbers, excluding 0 and 1, whose combined sum is less than or equal to the specified value. The list is returned in descending sequential order. The function also returns as a second value the sum of the list. NB: In addition to excluding 0 and 1, this function also differs from the plain fibonacci function in that the second value returned is the sum of the list rather than the first Fibonacci number greater than that sum.

ARGUMENTS

A number that is to be the test number.

RETURN VALUE

A list of descending sequential Fibonacci numbers, of which list the last element is 2. Also returns as a second result the sum of the list.

EXAMPLE

;; Returns a list whose sum is less than or equal to the number specified as ;; the function's only argument (fibonacci-start-at-217) => (5 3 2), 10 (fibonacci-start-at-220) => (8 5 3 2), 18 ;; Two examples showing the different results of fibonacci ;; vs.fibonacci-start-at-2;; 1 (fibonacci 18) => (5 3 2 1 1 0), 13 (fibonacci-start-at-218) => (8 5 3 2), 18 ;; 2 (fibonacci 20) => (8 5 3 2 1 1 0), 21 (fibonacci-start-at-220) => (8 5 3 2), 18

SYNOPSIS

(defunfibonacci-start-at-2(max-sum)

## l-for-lookup/fibonacci-transition [ Functions ]

[ Top ] [ l-for-lookup ] [ Functions ]

DESCRIPTION

Uses Fibonacci relationships to produces a sequence that is a gradual transition from one repeating state to a second over n repetitions. The function gradually increases the frequency of the second repeating state until it completely dominates. NB: The similar but separate function fibonacci-transition-aux1 gradually decreases state 1 and increases state 2.

ARGUMENTS

- An integer that is the desired number of elements in the resulting list (i.e., the number of repetitions over which the transition is to occur).

OPTIONAL ARGUMENTS

- Repeating item 1 (starting state). This can be any Lisp type, including lists. Default = 0. - Repeating item 2 (target state): This can also be any Lisp type. Default = 1. - T or NIL to make a morph from item1 to item2. This means morphing items will be a morph structure. See below for an example. Default = NIL. - T or NIL to make the morph first go down from item2 to item1 (mainly used by fibonacci-transitions). This can also be an envelope (see fibonacci-transitions for details). Default = NIL.

RETURN VALUE

A list.

EXAMPLE

;; Defaults to 0 and 1 (no optional arguments) (fibonacci-transition31) => (0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1) ;; Using optional arguments set to numbers (fibonacci-transition23 11 37) => (11 11 11 11 37 11 11 37 11 37 11 37 11 37 37 11 37 11 37 11 37 37 37) ;; Using lists (fibonacci-transition27 '(1 2 3) '(5 6 7)) => ((1 2 3) (1 2 3) (1 2 3) (1 2 3) (5 6 7) (1 2 3) (1 2 3) (5 6 7) (1 2 3) (1 2 3) (5 6 7) (1 2 3) (5 6 7) (1 2 3) (5 6 7) (1 2 3) (5 6 7) (5 6 7) (1 2 3) (5 6 7) (5 6 7) (1 2 3) (5 6 7) (5 6 7) (5 6 7) (5 6 7) (5 6 7)) ;; with morph: first going up then up/down (fibonacci-transition31 0 1 t) -> (0 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.14285714285714285d0) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.2857142857142857d0) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.42857142857142855d0) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.5714285714285714d0) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.7142857142857142d0) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.857142857142857d0) 1 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.8) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.6) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.4) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.7) 1 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.7) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.85) 1 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.75) 1 1 1 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.75) 1 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.75) 1 1 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.75) 1 1 1 1 1) ;; morph goes down then up (fibonacci-transition31 0 1 t t) --> (0 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.6666666666666667d0) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.3333333333333334d0) #S(MORPH :I1 0 :I2 1 :PROPORTION 1.1102230246251565d-16) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.25d0) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.5d0) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.75d0) 1 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.8) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.6) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.4) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.7) 1 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.7) #S(MORPH :I1 0 :I2 1 :PROPORTION 0.85) 1 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.75) 1 1 1 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.75) 1 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.75) 1 1 #S(MORPH :I1 0 :I2 1 :PROPORTION 0.75) 1 1 1 1 1)

SYNOPSIS

(defunfibonacci-transition(num-items &optional (item1 0) (item2 1) morph first-down)

## l-for-lookup/fibonacci-transitions [ Functions ]

[ Top ] [ l-for-lookup ] [ Functions ]

DATE

18 Feb 2010

DESCRIPTION

This function builds on the concept of the function fibonacci-transition by allowing multiple consecutive transitions over a specified number of repetitions. The function either produces sequences consisting of transitions from each consecutive increasing number to its upper neighbor, starting from 0 and continuing through a specified number of integers, or it can be used to produce a sequence by transitioning between each element of a user-specified list of items.

ARGUMENTS

- An integer indicating the number of repetitions over which the transitions are to be performed. - Either: - An integer indicating the number of consecutive values, starting from 0, the function is to transition (i.e. 3 will produce a sequence that transitions from 0 to 1, then from 1 to 2 and finally from 2 to 3), or - A list of items of any type (including lists) through which the function is to transition.

OPTIONAL ARGUMENTS

- T or NIL to make a morph from item1 to item2, 2 to 3, etc.. This means morphing items will be a morph structure. This can also be an envelope which thus allows morphing to be switched on and off over the course of the transition. The envelope can have any x range but the y-range should be from 0 to 1. Any value < 1 means the morph object will be ignored and either the :i1 or :i2 slot will be used instead, depending on whether the :proportion slot is > 0.5

RETURN VALUE

A list.

EXAMPLE

;; Using just an integer transitions from 0 to 1 below that integer (fibonacci-transitions76 4) => (0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 2 1 1 2 1 2 1 2 2 1 2 1 2 2 2 2 2 2 2 3 2 2 3 2 3 2 3 3 2 3 2 3 3 3 2 3 3 3 3 3 3 3 3 3 3) ;; Using a list transitions consecutively through that list (fibonacci-transitions152 '(1 2 3 4)) => (1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1 2 1 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 3 2 2 3 2 2 3 2 3 2 3 3 2 3 2 3 3 2 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3 3 4 3 3 4 3 3 4 3 4 3 4 4 3 4 3 4 4 3 4 4 3 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4) ;; A list of lists is also viable (fibonacci-transitions45 '((1 2 3) (4 5 4) (3 2 1))) => ((1 2 3) (1 2 3) (1 2 3) (1 2 3) (1 2 3) (4 5 4) (1 2 3) (1 2 3) (4 5 4) (1 2 3) (4 5 4) (1 2 3) (4 5 4) (1 2 3) (4 5 4) (1 2 3) (4 5 4) (1 2 3) (4 5 4) (4 5 4) (4 5 4) (4 5 4) (4 5 4) (3 2 1) (4 5 4) (3 2 1) (4 5 4) (3 2 1) (4 5 4) (3 2 1) (4 5 4) (3 2 1) (4 5 4) (3 2 1) (3 2 1) (3 2 1) (4 5 4) (3 2 1) (3 2 1) (3 2 1) (3 2 1) (3 2 1) (3 2 1) (3 2 1) (3 2 1)) ;; using morph (fibonacci-transitions52 '(1 2 3) t) => (1 #S(MORPH :I1 1 :I2 2 :PROPORTION 0.16666666666666666d0) #S(MORPH :I1 1 :I2 2 :PROPORTION 0.3333333333333333d0) #S(MORPH :I1 1 :I2 2 :PROPORTION 0.5d0) #S(MORPH :I1 1 :I2 2 :PROPORTION 0.6666666666666666d0) #S(MORPH :I1 1 :I2 2 :PROPORTION 0.8333333333333333d0) 2 #S(MORPH :I1 1 :I2 2 :PROPORTION 0.9) #S(MORPH :I1 1 :I2 2 :PROPORTION 0.5d0) #S(MORPH :I1 1 :I2 2 :PROPORTION 0.0d0) #S(MORPH :I1 1 :I2 2 :PROPORTION 0.5d0) 2 #S(MORPH :I1 1 :I2 2 :PROPORTION 0.7) #S(MORPH :I1 1 :I2 2 :PROPORTION 0.85) 2 #S(MORPH :I1 1 :I2 2 :PROPORTION 0.75) 2 2 2 #S(MORPH :I1 1 :I2 2 :PROPORTION 0.75) 2 #S(MORPH :I1 1 :I2 2 :PROPORTION 0.75) 2 2 2 2 #S(MORPH :I1 2 :I2 3 :PROPORTION 0.25d0) #S(MORPH :I1 2 :I2 3 :PROPORTION 0.5d0) #S(MORPH :I1 2 :I2 3 :PROPORTION 0.75d0) 3 #S(MORPH :I1 2 :I2 3 :PROPORTION 0.7) #S(MORPH :I1 2 :I2 3 :PROPORTION 0.85) 3 #S(MORPH :I1 2 :I2 3 :PROPORTION 0.75) 3 3 #S(MORPH :I1 2 :I2 3 :PROPORTION 0.75) 3 #S(MORPH :I1 2 :I2 3 :PROPORTION 0.75) 3 3 3 #S(MORPH :I1 2 :I2 3 :PROPORTION 0.75) 3 3 3 3 3 3 3 3 3) ;; using morph and a morph envelope (fibonacci-transitions52 '(1 2 3 3) '(0 0 10 1 52 1)) => (1 1 1 1 2 2 2 2 1 1 1 2 #S(MORPH :I1 1 :I2 2 :PROPORTION 0.7) #S(MORPH :I1 1 :I2 2 :PROPORTION 0.85) 2 #S(MORPH :I1 1 :I2 2 :PROPORTION 0.75) 2 2 2 #S(MORPH :I1 1 :I2 2 :PROPORTION 0.75) 2 #S(MORPH :I1 1 :I2 2 :PROPORTION 0.75) 2 2 2 2 2 2 3 3 #S(MORPH :I1 2 :I2 3 :PROPORTION 0.7) #S(MORPH :I1 2 :I2 3 :PROPORTION 0.85) 3 #S(MORPH :I1 2 :I2 3 :PROPORTION 0.75) 3 3 #S(MORPH :I1 2 :I2 3 :PROPORTION 0.75) 3 #S(MORPH :I1 2 :I2 3 :PROPORTION 0.75) 3 3 3 #S(MORPH :I1 2 :I2 3 :PROPORTION 0.75) 3 3 3 3 3 3 3 3 3)

SYNOPSIS

(defunfibonacci-transitions(total-items levels &optional morph)

## l-for-lookup/get-l-sequence [ Methods ]

[ Top ] [ l-for-lookup ] [ Methods ]

DESCRIPTION

Return an L-sequence of the key-ids for the rules of a given l-for-lookup object, created using the rules of that object. This method can be called with an l-for-lookup object that contains no sequences, as it only returns a list of the key-ids for the object's rules. Tip: It seems that systems where one rule key yields all other keys as a result makes for evenly distributed results which are different for each seed.

ARGUMENTS

- An l-for-lookup object. - The start seed, or axiom, that is the initial state of the L-system. This must be the key-id of one of the sequences. - An integer that is the length of the sequence to be returned. NB: This number does not indicate the number of L-system passes, but only the number of elements in the list returned, which may be the first segment of a sequence returned by a pass that actually generates a much longer sequence.

RETURN VALUE

A list that is the L-sequence of rule key-ids. The second value returned is a count of each of the rule keys in the sequence created, in their given order.

EXAMPLE

;; Create an l-for-lookup object with three rules and generate a new sequence ;; of 29 rule keys from those rules. The l-for-lookup object here has been ;; created with the SEQUENCES argument set to NIL, as theget-l-sequence;; method requires no sequences. The second list returned indicates the ;; number of times each key appears in the resulting sequence (thus 1 appears 5 ;; times, 2 appears 12 times etc.) (let ((lfl (make-l-for-lookup 'lfl-test NIL '((1 (2)) (2 (1 3)) (3 (3 2)))))) (get-l-sequencelfl 1 29)) => (2 3 2 3 2 1 3 2 3 2 3 2 1 3 2 3 2 1 3 3 2 1 3 2 3 2 3 2 1), (5 12 12) ;; A similar example using symbols rather than numbers as keys and data (let ((lfl (make-l-for-lookup 'lfl-test NIL '((a (b)) (b (a c)) (c (c b)))))) (get-l-sequencelfl 'a 19)) => (A C C B A C C B A C B C B A C C B A C), (5 5 9)

SYNOPSIS

(defmethodget-l-sequence((lflu l-for-lookup) seed stop-length)

## l-for-lookup/get-linear-sequence [ Methods ]

[ Top ] [ l-for-lookup ] [ Methods ]

DESCRIPTION

Instead of creating L-sequences with specified rules, use them generate a simple sequential list. The method first returns the first element in the list whose ID matches the SEED argument, then that element is used as the ID for the next look-up. Each time a rule is accessed, the next element in the rule is returned (if there is more than one), cycling to the head of the list once its end is reached. Seen very loosely, this method functions a bit like a first-order Markov chain, but without the randomness.

ARGUMENTS

- An l-for-lookup object. - The seed, which is the starting key for the resulting sequence. This must be the key-ID of one of the sequences. - An integer that is the number of elements to be in the resulting list.

OPTIONAL ARGUMENTS

- T or NIL to indicate whether to reset the pointers of the given circular lists before proceeding. T = reset. Default = T. - T or NIL to indicate whether to warn if any of the given keys are not used. Default = T.

RETURN VALUE

Two values: A list of results of user-defined length and the distribution of the results.

EXAMPLE

(let ((lfl (make-l-for-lookup 'lfl-test nil '((1 (2 3)) (2 (3 1 2)) (3 (1)))))) (get-linear-sequencelfl 1 23)) => (1 2 3 1 3 1 2 1 3 1 2 2 3 1 3 1 2 1 3 1 2 2 3)

SYNOPSIS

(defmethodget-linear-sequence((lflu l-for-lookup) seed stop-length &optional (reset t) (warn t))

## l-for-lookup/make-l-for-lookup [ Functions ]

[ Top ] [ l-for-lookup ] [ Functions ]

DESCRIPTION

Create an l-for-lookup object. The l-for-lookup object uses techniques associated with Lindenmayer-systems (or L-systems) by storing a series of rules about how to produce new, self-referential sequences from the data of original, shorter sequences. NB: This method just stores the data concerning sequences and rules. To manipulate the data and create new sequences, see do-lookup or get-l-sequence etc.

ARGUMENTS

- A symbol that will be the object's ID. - A sequence (list) or list of sequences, that serve(s) as the initial material, from which the new sequence is to be produced. - A production rule or list of production rules, each consisting of a predecessor and a successor, defining how to expand and replace the individual predecessor items.

OPTIONAL ARGUMENTS

keyword arguments: - :auto-check-redundancy. Some rules (e.g. in simplest form, a set of keys that return only one result each) will return a result of the same length no matter how many results we ask for. This can sometimes be problematic so do a check if requested. Default = NIL. - :scaler. Factor by which to scale the values returned by do-lookup. Default = 1. Does not modify the original data. - :offset. Number to be added to values returned by do-lookup (after they are scaled). Default = NIL. Does not modify the original data.

RETURN VALUE

Returns an l-for-lookup object.

EXAMPLE

;; Create an l-for-lookup object based on the Lindenmayer rules (A->AB) and ;; (B->A), using the defaults for the keyword arguments (make-l-for-lookup'l-sys-a '((1 ((a))) (2 ((b)))) '((1 (1 2)) (2 (1)))) => L-FOR-LOOKUP: [...] l-sequence: NIL l-distribution: NIL ll-distribution: NIL group-indices: NIL scaler: 1 offset: 0 auto-check-redundancy: NIL ASSOC-LIST: warn-not-found T CIRCULAR-SCLIST: current 0 SCLIST: sclist-length: 2, bounds-alert: T, copy: T LINKED-NAMED-OBJECT: previous: NIL, this: NIL, next: NIL NAMED-OBJECT: id: L-SYS-A, tag: NIL, data: ( [...] ;; A larger list of sequences, with keyword arguments specified (make-l-for-lookup'lfl-test '((1 ((2 3 4) (5 6 7))) (2 ((3 4 5) (6 7 8))) (3 ((4 5 6) (7 8 9)))) '((1 (3)) (2 (3 1)) (3 (1 2))) :scaler 1 :offset 0 :auto-check-redundancy nil)

SYNOPSIS

(defunmake-l-for-lookup(id sequences rules &key (auto-check-redundancy nil) (offset 0) (scaler 1))

## l-for-lookup/remix-in [ Functions ]

[ Top ] [ l-for-lookup ] [ Functions ]

DESCRIPTION

Given a list (for example generated by fibonacci-transitions) where we proceed sequentially through adjacent elements, begin occasionally mixing earlier elements of the list back into the original list once we've reached the third unique element in the original list. The earlier elements are mixed back in sequentially (the list is mixed back into itself), starting at the beginning of the original list, and inserted at automatically selected positions within the original list. This process results in a longer list than the original, as earlier elements are spliced in, without removing the original elements and their order. If however the :replace keyword is set to T, then at the selected positions those original elements will be replaced by the earlier elements. This could of course disturb the appearance of particular results and patterns. The :remix-in-fib-seed argument determines how often an earlier element is re-inserted into the original list. The lower the number, the more often an earlier element is mixed back in. A value of 1 or 2 will result in each earlier element being inserted after every element of the original (once the third element of the original has been reached). NB: The affects of this method are less evident on short lists.

ARGUMENTS

- A list.

OPTIONAL ARGUMENTS

keyword arguments: - :remix-in-fib-seed. A number that indicates how frequently an earlier element will be mixed back into the original list. The higher the number, the less often earlier elements are remixed in. Default = 13. - :mirror. T or NIL to indicate whether the method should pass backwards through the original list once it has reached the end. T = pass backwards. Default = NIL. - :test. The function used to determine the third element in the list. This function must be able to compare whatever data type is in the list. Default = #'eql. - :replace. If T, retain the original length of the list by replacing items rather than splicing them in (see above). Default = NIL.

RETURN VALUE

Returns a new list.

EXAMPLE

;; Straightforward usage with default values (remix-in(fibonacci-transitions 320 '(1 2 3 4 5))) => (1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 1 2 2 1 2 2 1 2 1 3 1 2 2 1 2 1 2 1 3 2 2 1 3 2 1 2 3 1 2 1 3 1 2 3 1 2 1 3 1 2 3 2 1 3 2 1 3 2 1 3 1 3 1 2 3 1 3 1 2 1 3 3 3 2 3 2 1 3 3 1 3 1 3 1 3 3 1 3 1 3 1 3 3 3 1 3 3 1 3 3 1 3 1 3 1 3 3 2 3 1 4 1 3 3 3 1 3 3 1 3 3 1 4 1 3 1 3 3 2 3 1 4 1 3 3 4 1 3 3 1 4 3 2 4 1 3 1 4 3 2 4 1 3 1 4 3 4 2 3 4 1 3 4 2 4 1 3 2 4 4 1 3 2 4 1 4 4 4 2 3 4 1 4 4 2 4 1 4 2 4 4 1 4 2 4 2 4 4 4 1 4 4 2 4 4 2 4 1 4 2 4 4 2 5 2 4 2 4 4 4 1 4 4 2 4 5 2 4 2 4 2 4 4 2 5 2 4 2 4 5 4 2 4 5 2 4 5 2 4 2 5 2 4 5 2 4 2 5 2 4 5 4 2 5 4 2 5 5 2 4 2 5 2 5 4 3 5 2 5 2 5 5 4 2 5 5 2 5 5 2 5 2 5 2 5 5 3 4 2 5 2 5 5 5 2 5 5 2 5 5 3 5 2 5 2 5 5 3 5 2 5 2 5 5 5 3 5 5 2 5 5 3 5 2 5 3 5 5 2 5 3 5 2 5 5 5 3 5 5 2 5 5 3 5 2 5 3 5 5 2) ;; A lower :remix-in-fib-seed value causes the list to be mixed back into ;; itself at more frequent intervals (remix-in(fibonacci-transitions 320 '(1 2 3 4 5)) :remix-in-fib-seed 3) => (1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 1 2 1 2 2 1 2 1 2 2 1 3 1 2 2 1 2 1 2 3 1 2 1 2 3 1 2 1 2 3 1 2 1 3 2 1 3 1 2 3 1 2 1 3 2 1 3 1 2 3 1 2 1 3 3 1 2 1 3 3 2 2 1 3 3 1 3 1 3 2 1 3 1 3 3 1 3 1 3 3 1 3 1 3 3 1 3 1 3 3 1 3 2 3 3 1 3 1 3 3 1 3 1 3 4 1 3 1 3 3 1 3 2 3 3 1 3 1 4 3 1 3 1 3 3 2 4 1 3 3 1 4 2 3 3 1 4 1 3 4 2 3 1 4 3 2 4 1 3 4 2 3 1 4 3 2 4 1 3 4 2 4 1 3 4 2 4 1 3 4 2 4 1 4 4 2 3 2 4 4 1 4 2 4 4 2 4 1 4 4 2 4 2 4 4 2 4 2 4 4 1 4 2 4 4 2 4 2 4 4 2 5 2 4 4 2 4 2 4 4 2 4 2 4 5 2 4 2 4 4 2 4 2 5 4 2 4 2 5 4 2 4 2 5 4 2 5 2 4 5 2 4 3 5 4 2 5 2 4 5 2 4 2 5 4 2 5 2 5 4 2 5 3 5 4 2 5 2 5 5 2 5 2 4 5 3 5 2 5 5 2 5 3 5 5 2 5 2 4 5 3 5 2 5 5 3 5 2 5 5 3 5 2 5 5 3 5 2 5 5 3 5 2 5 5 3 5 2 5 5 3 5 2 5 5 3 5 3 5 5 2 5 3 5 5 3 5 2 5 5 3 5 3 5 5 3 5 3 5 5 2 5 3) ;; Setting the keyword argument <mirror> to T causes the method to reverse back ;; through the original list after the end has been reached (remix-in(fibonacci-transitions 320 '(1 2 3 4 5)) :remix-in-fib-seed 3 :mirror t) => (1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 1 2 1 2 2 1 2 1 2 2 1 3 1 2 2 1 2 1 2 3 1 2 1 2 3 1 2 1 2 3 1 2 1 3 2 1 3 1 2 3 1 2 1 3 2 1 3 1 2 3 1 2 1 3 3 1 2 1 3 3 2 2 1 3 3 1 3 1 3 2 1 3 1 3 3 1 3 1 3 3 1 3 1 3 3 1 3 1 3 3 1 3 2 3 3 1 3 1 3 3 1 3 1 3 4 1 3 1 3 3 1 3 2 3 3 1 3 1 4 3 1 3 1 3 3 2 4 1 3 3 1 4 2 3 3 1 4 1 3 4 2 3 1 4 3 2 4 1 3 4 2 3 1 4 3 2 4 1 3 4 2 4 1 3 4 2 4 1 3 4 2 4 1 4 4 2 3 2 4 4 1 4 2 4 4 2 4 1 4 4 2 4 2 4 4 2 4 2 4 4 1 4 2 4 4 2 4 2 4 4 2 5 2 4 4 2 4 2 4 4 2 4 2 4 5 2 4 2 4 4 2 4 2 5 4 2 4 2 5 4 2 4 2 5 4 2 5 2 4 5 2 4 3 5 4 2 5 2 4 5 2 4 2 5 4 2 5 2 5 4 2 5 3 5 4 2 5 2 5 5 2 5 2 4 5 3 5 2 5 5 2 5 3 5 5 2 5 2 4 5 3 5 2 5 5 3 5 2 5 5 3 5 2 5 5 3 5 2 5 5 3 5 2 5 5 3 5 2 5 5 3 5 2 5 5 3 5 3 5 5 2 5 3 5 5 3 5 2 5 5 3 5 3 5 5 3 5 3 5 5 2 5 3 5 5 3 5 3 5 5 3 5 3 5 5 3 5 3 5 5 3 5 3 5 5 3 5 3 5 5 3 5 3 5 5 3 5 3 5 5 3 5 3 5 5 3 5 3 5 5 3 5 4 5 5 3 5 3 5 5 3 5 3 5 4 3 5 3 5 5 3 5 4 5 5 3 5 3 5 4 3 5 3 5 5 4 5 3 4 5 3 5 4 4 5 3 5 3 4 5 4 4 3 5 4 4 5 3 4 5 4 4 3 5 4 4 5 3 4 5 4 4 3 4 5 4 4 3 4 5 4 4 3 4 4 4 4 4 5 4 3 4 4 4 4 4 4 3 4 4 4 5 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 3 4 4 4 4 3 4 4 4 4 3 4 4 4 3 4 4 3 5 4 3 4 4 4 3 4 4 3 4 4 3 4 4 4 3 3 4 4 5 3 3 4 4 4 3 3 4 3 4 3 4 5 3 4 3 3 4 3 5 3 3 4 3 4 4 3 5 3 4 3 3 5 3 4 3 3 5 3 4 3 3 5 3 4 3 3 5 3 4 3 3 5 3 4 3 3 5 3 4 2 3 5 3 5 3 3 4 2 5 3 3 5 2 4 3 3 5 2 5 3 2 5 3 5 2 3 4 2 5 3 2 5 3 5 2 3 5 2 5 3 2 5 2 5 3 2 5 2 4 3 2 5 2 5 2 2 5 3 5 2 2 5 2 5 2 2 5 2 5 2 3 5 2 5 2 2 5 2 5 2 2 5 2 5 2 2 5 2 5 2 2 5 2 5 2 2 5 2 5 2 2 5 2 5 2 1 5 2 5 2 2 5 2 5 1 2 5 2 5 1 2 5 2 5 1 2 5 1 5 2 1 5 2 5 1 2 5 1 5 2 1 5 2 5 1 2 5 1 5 1 2 5 1 5 1 2 5 1 5 1 1 5 1 5 2 1 5 1 5 1 1 5 1 5 1 1 5 2 5 1 1 5 1 5 1 1 5 1 5 1 1 5 1 5 1 1 5 1 5 2 1 5 1 5 1 1 5 1 5 1 1 5 1 5 1 1 5 1 5 1 1 5 1 5 1 1 5 1 5 1 1 5 1 5 1 1 5 1 4 1)

SYNOPSIS

(defunremix-in(list &key (remix-in-fib-seed 13) (mirror nil) (test #'eql) (replace nil))

## l-for-lookup/reset [ Methods ]

[ Top ] [ l-for-lookup ] [ Methods ]

DESCRIPTION

Sets the counters (index pointers) of all circular-sclist objects stored within a given l-for-lookup object back to zero.

ARGUMENTS

- An l-for-lookup object.

OPTIONAL ARGUMENTS

- (an optional IGNORE argument for internal use only).

RETURN VALUE

Always T.

SYNOPSIS

(defmethodreset((lflu l-for-lookup) &optional ignore1 ignore2)