SELF-ORGANIZING TOPOLOGIES FOR SPATIAL DESCRIPTION

Space can cognise itself from elements of social system and can be self-generative at the same time. Architectural space can be visualized as an autonomous, adaptive and intelligent-complex system coupled with other autonomous complex system. Adaptive behaviour of autonomous artificial system of growing neural gas is exploited as a model of cognitive process for built environment. Cognition can be defined in terms of ability to respond to the environmental events, and the ‘stimulus’ is the part of environment that is absorbed by the structure of the model. Space can be expanded, deformed, fragmented, decayed and above all self-organized by learning from constituent of environment. Programs or events can be constructed by combination of actions and can be represented as point intensity on probability space. Space is constructed by intentional actions of individuals. Growing neural gas can be viewed as a ‘distributed representation technique for the spatial description’ of space, can learn and adapt itself according to point intensity on space. Different space – time conditions can create topological displacement and variation in spatial character. In general, the discussion is about the morphology of growing neural gas as an artificial autopoietic system and how it can couple to relevant features of the environment, as a two-way learning mechanism. The model’s synergetic construction of topology is a mental construction towards a theory of space. Space can be viewed as open, complex and self-organizing system, which exhibits phenomena of non-linearity and phase-transition. The notion of spatial cognition Spatiality refers to mental perception of space, mapping environment and behaviour. Spatial analysis is about the interrelationships between behaviour and properties of the manmade environment. It is about the techniques that objectively describe environments. This description can be related to specific local level phenomena of human behaviour such as vision, movement, perception, action or particular global phenomena of complex system. Cognition or ‘knowing’ is the perception of environmental change. It is the design process in nature and artificially intelligent system. Pointed out by Herbert Simon, any entity, be it natural or artificial, that devises courses of action aimed at changing existing situations into preferred ones (whatever they might be), can be said to engage in design activity [Simon, 1981]. 8 Generative Art Conference GA2005 Page 3 Cognition can be modelled as the embodied, evolving, and interaction of a self-organizing system with its environment as a design process in nature. Time-dependent cognition is an essential component of life or artificial life. All living systems or artificially living systems are cognitive systems. Cognition is simply the process of maintaining itself by acting in the environment. Maturana and Varela define 'cognition' in terms of basic ability to respond to environmental events. Design is a cognitive activity that all humans, other living beings, and the intelligent machines, are engaged in. The nature of design activity is highly diversified, as the underlying cognitive processes involved in different domains are fundamentally different. Space is a container, and action is what we do within it. A kind of natural geometry is generated by actions and movements on space. As an example, a group collectively define a space in which people can see each other, mathematician defines it as ‘convexity of space’, and represents it by points on space. Formal and spatial aspects of architectural and urban design are known as ‘configurational’ research techniques, which can easily be turned round and can be used to support experimentation and simulation in design. This way is one kind of attempt to subject ‘the pattern aspect of elements in architecture’ to rational analysis, and to test the analysis by embodying them in real designs. Spatial scales can be local and global. The local scale deals with immediate neighbours and global scale deals with overall spatial configuration. Graph-based topological model in archiectural spatial analysis Graph-based operationalizations of space, which are used for mental representations of environment in the field of architecture and cognitive science, describe environment by means of nodes and edges, roughly represent to spaces and their spatial relations. Edges implement relationship between nodes. Graph-based model is flexible, extendable, and its’ generic framework with straightforward algorithms help to solve specific higher-level questions regarding architectural spatial issues. Mental representations of space cannot be seen independently from the formal and configerational properties of the corresponding environments. At the same time, formal description of a space as used in architecture gain rationality by incorporating results from cognitive research, which give the prediction and explanation of actual behaviour of the system. Graphbased diagrammatic analysis deals with theory of space gives quantitative expression to ‘elusive pattern aspect’ of architectural and urban design. It is a ‘neutral techniques’ for the description and analysis of the ‘non-discursive’ aspects of space and form. Graph based models are used for quantitative comparisons between spatial configurations in order to identify the essential properties in terms of function or usage. It is considered as strictly formalized description system of space. Beside applied research, graph investigations in architecture particularly concentrated on methodological issues such as the analysis techniques on arbitrarily shaped environments on variable scale levels and on the formalization and automation of the graph generation process within certain complex spatial system.Turner, Dexa, O’Sullivan, & Penn (2001) have proposed visibility graphs in different way to optimise the computational graph analysis. Visibility graphs replace the isovist as node content by inter-visibility information translated into edges to other nodes. Visibility graphs are useful to predict spatial behaviour and affective qualities of indoor spaces. 8 Generative Art Conference GA2005 Page 4 Neural networks and graph-based topological representation Knowledge is acquired by the network from its environment through a learning process and Interneuron connection strengths are used to represent the acquired knowledge. The every single unit could be the metaphoric representation of an individual entity and lines could be communication links. A neural network can be represented as a graph consisting of nodes with interconnecting synaptic and activation links. Self-organizing neural network: Growing Neural Gas Self –organizing neural network models were first proposed by Willshaw & vonder Mlalsburg (1976) and Kohonen (1982). The networks generate mappings from high-dimensional signal spaces to lower dimensional topological structures. The “growing neural gas” algorithm of Martinetz & Schulten (1994) seems to produce compact networks, which preserve the neighbourhood relations extremely well. The network has a flexible as well as compact structure, a variable number of elements, and a Kdimensional topology. The algorithm is considered as spetio-temporal Event Mapping (STEM) architecture. It can be viewed as decentralized model of human brain learning process or decentralized model of cognition. Martinetz (1994) introduced a class of Topology Representing Networks (TRN), which belongs to Dynamic Cell Structures (DCS), build perfectly topology preserving feature map. DCS idea applied to the Growing Cell Structure algorithm (Fritzke 93) is a more efficient and elegant algorithm than conventional models on similar task. Growing Neural Gas (GNG) is a class of Growing Cell Structure. It differs from Growing Cell Structure through its less rigid topological definition. GNG only uses the parameters that are constant in time. It employs a modified Kohonen Learning rule (unsupervised) combine with competitive Hebbian learning. The kohonen type learning rule serves to adjust the synaptic weight vectors and Hebbian learning establishes a dynamic lateral connection structure between the units. The new model of growing neural gas can be said the extension of Kohonen’s feature map with respect to various important criteria (Fritzke, 1993a). Two basic differences with Kohonen SOM: 1 The adaptation strength is constant over time. Specifically used constant adaptation parameters e_b and e_n for the best matching unit and the neighbouring cells, respectively. 2 Only the best-matching unit and its direct topological neighbours are adapted. Neural gas as a connectionist model (Donald Hebb 1949) Brain operation can be modelled by means of a network of interconnected nodes. Each Node takes the sum of its inputs and generates an output. The output is determined by the transfer function of the node, which has to be non-linear. The connection (synapse) between any two nodes has certain ‘weight’. The information flows only in one direction. Complex behaviour emerges from the interaction between many simple processors that respond in a non-linear way to local information. 8 Generative Art Conference GA2005 Page 5 The characters of connectionist models are: 1 High level of interconnectivity 2 Recurrence 3 Distributedness (described algorithmically) sparsely connected fully connected richly connected GNG connectionist model consists of a large number of units, richly interconnected with feedback loops, but responding only to local information. The process of autopoiesis An answer lies in the pattern characteristic of all living systems is autopoiesis, a network pattern in which each node is a production process that produces or transforms other nodes. The entire network continually produces itself. The pattern & process of interaction are called autopoiesis & cognition. Thus, autopoiesis is the pattern by which life emerges in dissipative