GEOWIN

A System for Creative Pattern Generation based on Rules

Joaquim A. M. dos Reis

ISCTE, Dept. Ciências e Tecnologias de Informação, Av. das Forças Armadas, 1600 Lisboa, Portugal

Keywords: Rule-Based Systems, Shape Grammars, Design, Creativity.

Abstract: GEOWIN, a computational system based on rules for generating visual patterns is being developed and this

paper describes the work done so far. Rules are used to implement shape grammars to represent styles of

visual composition. This work is a continuation of previously published work addressing the construction of

a system employing shape grammar rules grouped to emulate styles of visual composition, in order to

support the behavior of different artistic creative intelligent agents with different styles. One of the goals of

this work is to have a multi-agent system that, by making use of the shape grammar formalism, will be able

to support creative visual composition synthesis activities, with each intervening agent giving its creative

contribution through a style of its own. Another goal is to use the system as a tool to realize, test and study

creativity criteria and creative processes.

1 INTRODUCTION

In this paper, we show work done and in progress in

implementing part of a system proposed in

previously published papers. See (Reis, 2006a),

(Reis, 2006b), (Reis, 2006c), (Reis, 2006d), (Reis,

2008a) and (Reis, 2008b), where we describe a

multi-agent system in which different artistic

creative intelligent agents, each with its own style,

are able to involve in artistic visual composition

activities, and where shape grammars are used to

emulate styles of visual composition of each agent.

We first expose some concepts centered around

computational creativity, then we introduce shape

grammars briefly, and finally we describe the work

done and the present state of the system

implementation.

By one side we are interested in having a tool to

generate alternative creative visual compositions

with specific styles, or mixture of styles (and, of

course, possible applications for this kind of system

could be visual composition generation with mixed

styles, either free generation or controlled and goal

oriented generation, e.g., technical drawing, Web

page layout design, output layout reconfiguration).

On the other side, we are also interested in studying

human creativity and computationally realize and

test creativity criteria and creative processes in

visual composition and design.

2 COMPUTATIONAL

CREATIVITY

Creativity is an important issue we want to address

and this is also because one of our goals is to help to

understand creativity. Can we make the computer (a

machine) to be creative or, at least, to emulate

human creativity? This is seems to be the main goal

in the area of computational creativity. But other

questions are raised too. What is creativity? And

how can we define it? And where does it com from?

What is a creative idea, or a creative artifact? Is it

just a new one, or a surprising new one, or a

valuable new one? This subject seems to be two

sided: one point of view is the study and

understanding of human creativity, the other is to

produce machine creativity and make computer to

be, or at least to appear to be, creative.

We can view creativity through two perspectives:

the combination-transformation perspective and the

personal-human perspective (Boden, 2004). The

former has to do with producing new ideas simply

by combining old ones - “improbabilistic” creativity

–, the latter consists in transforming completely the

manner in which the new ideas are produced (more

concretely the style used) - “impossibilistic”

creativity. In the former case, a new idea comes

from a new combination of familiar ideas

(specifically those combinations that we value,

289

A. M. dos Reis J. (2009).

GEOWIN - A System for Creative Pattern Generation based on Rules.

In Proceedings of the 4th International Conference on Software and Data Technologies, pages 289-296

DOI: 10.5220/0002240402890296

 SciTePress

because they are highly improbable or because of

some other kind of criterion). In the latter case a new

idea comes from a radically new generation process.

The personal-human perspective, has to do with

whether a new idea is new within the personal

context – personal, psychological, or P-creativity –

or within the whole human history context – human,

historic, or H-creativity. In the first case, an idea is

P-creative if the person in whose mind it occurred

never had that idea before. In the other case, not

only the idea had never occurred before in the mind

of the person but also no one had ever had that idea.

Two different additional questions, but practical

ones, about computational creativity concern to the

creativity criteria to evaluate new ideas and to the

generative process to produce the new idea (Ritchie,

2001).

3 SHAPE GRAMMARS

How does a creative agent, human or artificial, build

a composition step by step. That is to say, in each

state of the composition, how does the agent choose,

among the myriad of possible options, to proceed?

The generative processes of the system we proposed

in previously published papers, see (Reis, 2006a),

(Reis, 2006b), (Reis, 2006c), (Reis, 2006d), (Reis,

2008a) and (Reis, 2008b), are based on the shape

grammar formalism. Concerning the creativity

criteria, we assume it will be provided by the user as

she/he can intervene in the generative process.

Shape grammars were introduced in the 1970s by

Stiny and Gips (Stiny, 1972). They are similar in

principles to the grammars used in the area of

Natural Language Understanding and Generation of

Artificial Intelligence, with the difference of being

based not on symbols, but on shapes (points, lines,

two-dimensional and three-dimensional geometric

shapes) as well as, by extension, also other

parameters like dimensions, colors, etc..

A vocabulary of basic shapes, an initial shape

and a finite set of rules that specify how shapes can

be generated from other, preexistent, shapes are the

components of a shape grammar. These are an

analogue, respectively, of the lexicon, of the initial

symbol and of the grammar rules of a language in a

natural language processing system. The rules of a

shape grammar specify how, in a composition in

progress, shapes existing in the composition can

trigger the addition of new shapes. Each rule has a

left side, pre-condition, or antecedent, and a right

side, action, or consequent. The left side specifies

the pattern for which the rule is applicable and the

right side the respective pattern to add. Briefly, a

rule is applicable if there is a similarity

transformation (i.e., an isometric or a scale) leading

to a match of the shape of the left side of the rule

with a shape existing in the composition. Rules are

applied in a forward manner (from antecedent to

consequent), like in the production/rule-based

forward-chaining expert systems of Artificial

Intelligence, which perform a kind of forward

inference. When applied, a rule adds the shapes in its

right side.

Shape grammars have been used in different

design problems, in the context of synthesis

(generation) and analysis (interpretation) of visual

compositions and also as means to the description

and the representation of styles, including for

didactic purposes and also other specific

applications, for instance in architectural drawings

(Gips, 1999), (Tapia, 1999), (Knight, 2000),

(Mitchell, 1990). A style is a way of someone doing

something (Simon, 1971) and shows up when that

someone chooses an alternative or a process for

generating a solution. In the field of design, a style is

a kind of design knowledge which is a characteristic

of a product, or a set of products, of design, and is

recognizable through the presence of some visual

elements like shape, color, relative position, texture,

dimension, orientation (Dondis, 1973), (Bonsiepe,

1983), (Wong, 1993) as well as certain ways of

combining those elements. Visual compositions can

be generated automatically according to specific

styles. Each style can be implemented by a set of

rules of a specific shape grammar. Additional

information and theory about shape grammars can

be found in (Shape Grammars, 2006), where lists of

paper references, people and projects are included

too. In (Knight, 2000) we can also find the history of

applications of shape grammars in Architecture and

Arts and a discussion about the roles of shape

grammars in education and practice, as well as new

and ongoing issues. In (Chau, et.al., 2004) we can

find a survey of shape grammar implementations.

Work on the algebras of shapes and issues of shape

representation and recognition can be found in

(Chase, 1996), (Krishnamurti, 1992) and

(McCormack and Cagan, 2002). (Gross, 1996) and

(Gross, 1991) are examples of work involving

application to CAD and constraint based design.

Other papers on creativity modeling, computational

creativity and the relationship between art and

technology can be found in (Gero and Maher, 1993)

and (Candy and Edmonds, 2002).

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4 GEOWIN

GEOWIN, a prototype program of the system

described in the papers referred is being developed

in the programming language Common Lisp (Steele,

1990). We choose this programming language

because its exploratory and flexible object oriented

programming model and for allowing the production

of reusable and extensible software. GEOWIN

presently includes the FC (Forward-Chaining), the

GEO (GEOmetry) and the SG (Shape-Grammar)

modules of Lisp code. Agents are not yet

implemented.

(defun forward-chain ()

(do ((newfacts nil) (results t))

((null results) newfacts)

(setf results nil)

(dolist (rule (kb-rules)

(setf newfacts

(append results newfacts)))

(setf results

(append (use-rule rule)

results)))))

Figure 1: The forward-chain function.

A forward-chaining inference engine to drive

shape grammar rule application is implemented in

the FC module, which includes a small language to

express rules and facts. Rules are stored in the rule

memory part and facts are stored in the working

memory part of a knowledge base. In Figure 1. we

show the code for the function forward-chain,

the one that contains the main cycle of the FC

module. The function kb-rules returns a list of

applicable rules in the rule memory and the function

use-rule is then used to apply each of those rules

in each iteration of the dolist cycle, to generate

new facts. This is repeated (by means of a do cycle)

until no more new facts can be generated. As an

alternative to forward-chain the function

use-rule can also be used for selective and

incremental rule application.

(r1 "Horizontal rectangle rule."

(and (rectangle ?x1 ?y1 ?x2 ?y2

?color ?filledp)

(is ?length (- ?x2 ?x1))

(is ?height (- ?y2 ?y1))

(rh-hmin ?hmin) (rh-hmax ?hmax)

(rh-ratio-min ?rmin)

(rh-ratio-max ?rmax)

(<= ?hmin ?height ?hmax)

(<= ?rmin

(/ ?length ?height) ?rmax)

(rh-delta ?delta)

(is ?d (eval (floor

(/ ?height ?delta))))

(is ?x1a (- ?x2 ?d))

(is ?x2a (+ ?x1a ?length))

(is ?y1a (- ?y1 (- ?height ?d)))

(is ?y2a (+ ?y1a ?height))

(x-min ?xmin) (x-max ?xmax)

(y-min ?ymin) (y-max ?ymax)

(<= ?xmin ?x1a ?x2a ?xmax)

(<= ?ymin ?y1a ?y2a ?ymax))

(rectangle ?x1a ?y1a ?x2a ?y2a

dark-red t))

Figure 2: An example of a shape grammar

forward-chaining rule, rule r1.

An example of a rule is shown in Figure 2.. The

body of a rule has the antecedent and the consequent

section, before and after the symbol ->, respectively

besides the rule identifier, r1, and a documentation

string, as we can see. Facts are expressed as patterns

which are represented by Lisp lists. When a rule is

applied, each fact pattern, possibly containing rule

variables, in the antecedent part of the rule is

"pattern-matched" with facts in the working memory

part of the knowledge base. A successful

pattern-matching is expected to instantiate existing

rule variables in one or more ways. When appearing

in the consequent part a pattern means a new fact to

be added to the working memory in case the

pattern-matching process of the fact patterns in the

antecedent part of the rule was successful (any

variables in the fact pattern should have been then

instatiated).

When applied once the rule r1 shown identifies

a rectangle fact and, apart from a number of

constraint fact verifications (to exclude rectangles

that are not "horizontal" or have proportions outside

some intended limits and to avoid generation outside

the limits of the drawing area) generates a new

rectangle fact equal to the first one but lightly

translated.

GEOWIN - A System for Creative Pattern Generation based on Rules

291

Figure 3: Rule r1 ("horizontal" rectangle) generation

example. Generated shapes are solid, the start shape is the

clear rectangle.

In Figure 3. we show the result of some

successive aplications of rule r1, given an initial

rectangle shape.

(r3 "Square rule."

(and (rectangle ?x1 ?y1 ?x2 ?y2

?color ?filledp)

(is ?a (- ?x2 ?x1))

(is ?height (- ?y2 ?y1))

(= ?a ?height) (rq-amin ?amin)

(>= ?a ?amin) (rq-delta ?delta)

(is ?d (eval (floor

(/ ?a ?delta))))

(is ?x1a (+ ?x1 ?d))

(is ?x2a ?x2)

(is ?y1a (- ?y1 ?a))

(is ?y2a (- ?y2 (+ ?a ?d)))

(x-min ?xmin) (x-max ?xmax)

(y-min ?ymin) (y-max ?ymax)

(<= ?xmin ?x1a ?x2a ?xmax)

(<= ?ymin ?y1a ?y2a ?ymax))

(rectangle ?x1a ?y1a ?x2a ?y2a

green t))

Figure 4. Another example of a shape grammar

forward-chaining rule, rule r3.

In Figure 4. and Figure 5., we show additional

rule examples, respectively rule r3, which, in the

presence of a square, adds another one, scaled down

and translated, and rule r4, which, in the presence

of a two shape pattern (a "horizontal" rectangle and

a square, lightly superinposed) adds a small circle.

(r4 "Horizontal rectangle, square

and

circle rule."

(and (rectangle ?xr1 ?yr1 ?xr2 ?yr2

?color1 ?fillp1)

(is ?length (- ?xr2 ?xr1))

(is ?height (- ?yr2 ?yr1))

(rh-hmin ?hmin) (rh-hmax ?hmax)

(rh-ratio-min ?rmin)

(rh-ratio-max ?rmax)

(<= ?hmin ?height ?hmax)

(<= ?rmin (/ ?length ?height)

?rmax)

(rectangle ?xq1 ?yq1 ?xq2 ?yq2

?color2 ?fillp2)

(is ?a (- ?xq2 ?xq1))

(is ?aheight (- ?yq2 ?yq1))

(= ?a ?aheight) (rq-amin ?amin)

(>= ?a ?amin)

(is ?delta (- ?yq2 ?yr1))

(> ?height ?delta 0)

(> ?xr2 ?xq1 ?xr1)

(is ?r (eval (floor (/

(- ?height (* 3 ?delta)) 2))))

(> ?r 0)

(is ?xc (+ ?xr1 ?delta ?r))

(is ?yc (+ ?yr1 (* 2 ?delta)

?r)))

(circle ?xc ?yc ?r dark-blue t))

Figure 5. Another example of a shape grammar

forward-chaining rule, rule r4.

Rules r3 and r4 have their results exemplified

in Figure 6. and Figure 7., respectively.

Figure 6: Rule r3 (scaled square) generation example.

Generated shapes are solid, the start shape is the clear

rectangle.

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Additional examples of generation with rules for

which, for reasons of space, we don't show code, are

presented in Figure 8. and Figure 9.

Figure 7: Rule r4 ("horizontal" rectangle, square and

circle) generation example. Generated shapes are solid, the

start shape is the clear rectangle.

A fact is composed of the name of the predicate

and the arguments, possibly variables, as in

(rectangle ?x1 ?y1 ?x2 ?y2 ?color

?filledp). Symbols starting with a ? character

are rule variables. Apart from facts, the rule

language has special predefined operators, some of

which can be seen in the example. These operators

include the logical operators and, or and not (to

logically combine facts in the antecedent part of the

rule), arithmetic operators (+, -, * and /) and

comparators (=, /=, >, >=, < and <=), the operator

is for assignment (similar in nature to the is

operator in the Prolog programming language) and

an eval special operator to evaluate arbitrary Lisp

expressions, possibly containing rule variables.

Figure 8: Additional rule generation example.

Graphical shape representation and the graphical

environment and its interactive and programmatic

interfaces is implemented in the GEO module.

Geometric shapes are implemented through objects

of Common Lisp. The most general class is the

shape class, and there are classes for points, line

segments, rectangles and circles, all subclasses of

shape. In Figure 10. we show segments of code

including the definition of classes shape and

circle.

Figure 9: Another aditional rule generation example.

A user can create and introduce new points,

segments, rectangles and circles that appear in a

drawing area through the interactive interface. The

programmatic interface allows the same through

calls to the appropriate Lisp methods. In the near

future the interactive interface will be expanded to

allow also the creation new shape grammar rules

interactively. In Figure 3., Figure 6. and Figure 14..,

the window of the drawing area of the interface is

shown.

(defclass shape ()

((color :reader color :initarg :color

:initform nil)))

(defclass circle (shape)

((center :reader center

:initarg :center :type point)

(radius :reader radius

:initarg :radius :type integer)

(id :reader id

:initform (circle-id-calc))

(filledp :reader filledp

:initarg :filledp :initform nil))

(:documentation "Circle shape."))

Figure 10: Some class definitions of the GEO module.

GEOWIN - A System for Creative Pattern Generation based on Rules

293

An ontology of the geometric two-dimensional

domain, some relations of which were implemented

in the GEO module, was also defined. This ontology

includes geometric points and relative position

relations between geometric points along the x and

the y axes, line segments and relative position

relations between line segments along the x and the

y axes, and rectangular shapes and relative position

relations between rectangular shapes along the x and

y axes on the plane.

(defmethod x-before ((s1 shape)

(s2 shape))

(< (x-max s1) (x-min s2)))

(defmethod x-after ((s1 shape)

(s2 shape))

(< (x-max s2) (x-min s1)))

(defmethod x-meets ((s1 shape)

(s2 shape))

(= (x-max s1) (x-min s2)))

(defmethod y-equals ((s1 shape)

(s2 shape))

(and (= (y-min s1) (y-min s2))

(= (y-max s1) (y-max s2))))

Figure 11: Some of the methods for relative position

relations between shapes of the GEO ontology.

The ontology is described in the published

papers, and is reflected in the GEO module in Lisp

methods that implement the relations between

shapes, as shown in example segments of code in

Figure 11. (functions x-max, x-min, y-max,

and y-min produce the extreme x and y coordinate

values of a given shape).

Lastly, the SG module integrates the work done

by the two others. Essentially, the functions

contained in the SG module allow top level

introduction of new shapes in a composition,

introduction of new shape grammar rules and to start

the generation of a composition. Part of the code for

this functionality is shown in Figure 12.. Usually, a

set of parameters are previously established, by

means of facts added to the knowledge base, in order

to allow some rules to be aplicable. Also, some

shape grammar rules are added, as well as one or

more start shapes. Finaly, a generation can be run.

This is all accomplished through calls to SG

functions.

The entire process is exemplified in Figure 13.

for rule r1 (shown in Figure 2.), including adding a

rectangle as a start shape. Figure 3. shows the result

of the corresponding generation with rule r1. A

more elaborated generation example is shown in

Figure 14., involving five shape grammar rules

(including r1, r3, r4 and the rules exemplified in

Figure 8. and Figure9.) and two start shapes.

(defun sg-add-shape (fact &aux

newfact newshape)

(and *geowin*

(setf newfact

(sg-add-fact fact))

(setf newshape

(sg-add-shape-aux fact)))

(values newfact newshape))

(defun sg-add-rule (rule)

(assert-rule rule))

(defun sg-gen (&aux newfacts newshapes

tmpshp)

(and *geowin*

(setf newfacts (forward-chain))

(setf newshapes

(mapcan

#'(lambda (fact)

(and (setf tmpshp

(sg-add-shape-aux fact))

(list tmpshp)))

newfacts)))

(values newfacts newshapes))

Figure 12: Some of the functions of the SG module.

5 FUTURE WORK

Generically, future work will improve and refine the

GEWIN system, and will use it as a tool to realize

and test creativity criteria and creative processes. In

specific, we can point at some future work tasks

needed to be done.

One of those tasks respects to improvement of

the FC module. This can involve to improve and

optimize the pattern matching process and the other

forward-chaining functionalities, e.g., by using the

RETE algorithm, see (Forgy, 1982) or (Doorenbos,

1995), for instance.

The system will also evolve to a multi-agent one

after we have implemented agents. Each agent will

essentially be a forward-chaining subsystem with its

own knowledge base (some adjustments may be

necessary in the FC code for this). One of the most

significant aspects to give special attention to are the

control mechanisms for rule application, which can

be viewed in the intra-agent and in the inter-agent

perspectives. The latter involves the coordination of

the activity of the agents in the multi-agent system.

ICSOFT 2009 - 4th International Conference on Software and Data Technologies

294

(sg-ini) ; initialize system

;; graphic area limits:

(sg-add-fact '(x-min 0))

(sg-add-fact '(x-max 700))

(sg-add-fact '(y-min 0))

(sg-add-fact '(y-max 500))

;; matching constraints:

(sg-add-fact '(rh-hmin 20))

(sg-add-fact '(rh-hmax 50))

(sg-add-fact '(rh-ratio-min 2))

(sg-add-fact '(rh-ratio-max 5))

;; generation parameters:

(sg-add-fact '(rh-delta 2))

;; shape grammar rule:

(sg-add-rule

'(r1 "Horizontal rectangle rule."

(and (rectangle ?x1 ?y1 ?x2 ?y2

?color ?filledp)

(is ?length (- ?x2 ?x1))

(is ?height (- ?y2 ?y1))

(rh-hmin ?hmin)

(rh-hmax ?hmax)

(rh-ratio-min ?rmin)

(rh-ratio-max ?rmax)

(<= ?hmin ?height ?hmax)

(<= ?rmin (/ ?length ?height)

?rmax)

(rh-delta ?delta)

(is ?d (eval (floor

(/ ?height ?delta))))

(is ?x1a (- ?x2 ?d))

(is ?x2a (+ ?x1a ?length))

(is ?y1a (- ?y1

(- ?height ?d)))

(is ?y2a (+ ?y1a ?height))

(x-min ?xmin) (x-max ?xmax)

(y-min ?ymin) (y-max ?ymax)

(<= ?xmin ?x1a ?x2a ?xmax)

(<= ?ymin ?y1a ?y2a ?ymax))

(rectangle ?x1a ?y1a ?x2a ?y2a

dark-red t)))

;; start shape: "horizontal" rectangle:

(sg-add-shape '(rectangle 21 400 180

440 dark-red nil))

(sg-gen) ; start generation

Figure 13: Preparing and running a generation with rule

r1 using the programatic interface of the SG module.

Some work needs also to be done in the GEO

module involving some computational geometry

know-how. This will involve to expand the number

of geometric shape types the system can represent

and to have the possibility to edit and change

preexistent shape instances in the drawing area,

including by application of different geometric

Figure 14: Example of a composition involving several

rules. Generated shapes are solid, the start shapes are

clear

transformations.

The geometric shape manipulation referred

above, more specifically similarity transformations,

will be useful particularly for the recognition

mechanism of shape patterns in the antecedent part

of shape grammar rules. This mechanism is

presently limited to recognize a shape indicated

almost in a literal manner in the rule, with limited

provision to specify scale transformations (but at the

cost of using some extra programming in the

language of rules, as we could see by the example

rules shown before).

Still another task to be done at the level of GEO

is to program the interactive creation of new shape

grammar rules using the graphical interface.

6 CONCLUSIONS

In this paper we have shown work done and in

progress in developing a proposed computational

system based on rules for generating patterns for

visual composition. The system makes use of the

shape grammar concept, i.e., the rules can specify

geometric shape manipulations to produce new

shapes, given some initial one(s). Shape grammars

can be used to emulate styles of visual composition

which is an interesting idea that can be applied to

exploratory design. In the future we plan to evolve

the system to a multi-agent system to support visual

composition synthesis activities, with each

intervening agent giving its creative contribution

through a style of its own, and use the system as a

tool to our investigation in realizing and testing

GEOWIN - A System for Creative Pattern Generation based on Rules

295

creativity criteria and creative processes.

ACKNOWLEDGEMENTS

Research presented in this paper was partially

supported by FCT (the Portuguese Foundation for

Science and Technology).

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