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Figure 4.38: A conventional drawing of a Turing Machine.

Figure 4 38: A conventional drawing of a Turing Machine.

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Figure 1.1: Evolutionary Design comes at the intersection of three fields.
Figure 1.1: Evolutionary Design comes at the intersection of three fields.
Figure 1.2: The process of a genetic algorithm.
Figure 1.2: The process of a genetic algorithm.
are local maxima. Figure 1.3 shows such a landscape. The easiest search spac to visualise would be a population of solutions which had two parameters (o genes), each represented by a real number. If each of these genes was mapped t an axis (X and Y) and the fitness of the solution was mapped as its height (th Z-axis) then the highest point would correspond to the fittest solution. The ain of a genetic algorithm is to traverse this space moving across the smaller peak and valleys until the global maximum is reached. Most problems will have mor than two parameters and become much harder to visualise. than two parameters and become much harder to visualise. Figure 1.3: The space where solutions exist can be seen as a landscape.
are local maxima. Figure 1.3 shows such a landscape. The easiest search spac to visualise would be a population of solutions which had two parameters (o genes), each represented by a real number. If each of these genes was mapped t an axis (X and Y) and the fitness of the solution was mapped as its height (th Z-axis) then the highest point would correspond to the fittest solution. The ain of a genetic algorithm is to traverse this space moving across the smaller peak and valleys until the global maximum is reached. Most problems will have mor than two parameters and become much harder to visualise. than two parameters and become much harder to visualise. Figure 1.3: The space where solutions exist can be seen as a landscape.
The last step in designing an evolutionary system is to create a function for svaluating the fitness of each member of the population. The process need not oe entirely automated. It is possible to have a human user who participates in sche evaluation process, effectively breeding solutions as one would breed plants or animals to have particular characteristics. This approach was used in the hiomorphs example mentioned earlier as well as Rastogi and Frazer’s Interactiva- tor (Frazer et al. [1995]). An implementation of an evolutionary solver developed specifically for this dissertation is shown in Figure 1.4. Figure 1.4: Implementation of an Evolutionary Solver
The last step in designing an evolutionary system is to create a function for svaluating the fitness of each member of the population. The process need not oe entirely automated. It is possible to have a human user who participates in sche evaluation process, effectively breeding solutions as one would breed plants or animals to have particular characteristics. This approach was used in the hiomorphs example mentioned earlier as well as Rastogi and Frazer’s Interactiva- tor (Frazer et al. [1995]). An implementation of an evolutionary solver developed specifically for this dissertation is shown in Figure 1.4. Figure 1.4: Implementation of an Evolutionary Solver
Table 2.1: ] Examples of | Evolutionary Design
Table 2.1: ] Examples of | Evolutionary Design
Figure 2.1: Diagram after Alexander’s - the finding of sub-graphs.
Figure 2.1: Diagram after Alexander’s - the finding of sub-graphs.
Figure 2.2: Diagram after Alexander’s - Tree Diagram after decomposition
Figure 2.2: Diagram after Alexander’s - Tree Diagram after decomposition
Figure 2.4: Development of minor axes after Eisenman.
Figure 2.4: Development of minor axes after Eisenman.
Figure 2.3: Emphasising the main entry by a turn in the minor entry
Figure 2.3: Emphasising the main entry by a turn in the minor entry
Figure 2.5: Radiant heating cores define a static system.
Figure 2.5: Radiant heating cores define a static system.
Figure 2.6: The dominant cruciform pattern.
Figure 2.6: The dominant cruciform pattern.
Figure 2.7: Definition of two separate volumes by individual readings
Figure 2.7: Definition of two separate volumes by individual readings
Figure 2.8: Continuous reading of cores. From these extracts it can be gathered that the reasons that particular ar- chitectural forms exist are not merely for meeting functional requirements; nor are they dominated by some sort of compositional system alone. Within this lies the reason that this work being of interest to generative design. The representa- tions are moving closer to describing a type of ‘diagram’ or ‘system’ forming the conceptual underpinning that drives the architecture. As Eisenman writes: From these extracts it can be gathered that the reasons that particular ar-
Figure 2.8: Continuous reading of cores. From these extracts it can be gathered that the reasons that particular ar- chitectural forms exist are not merely for meeting functional requirements; nor are they dominated by some sort of compositional system alone. Within this lies the reason that this work being of interest to generative design. The representa- tions are moving closer to describing a type of ‘diagram’ or ‘system’ forming the conceptual underpinning that drives the architecture. As Eisenman writes: From these extracts it can be gathered that the reasons that particular ar-
numbers are used as abstractions to be used for mathematical operations in en gineering, geometry could be used for architecture Madrazo [1994]. Figure 2.1 below shows a plate with the title ‘Ensembles d’edifices resultants des division du quarre, du parallelogramme et de leurs cominaisons avec le cercle’ (plans re sulting from dissections of circle and square). This image shows diagrams only the essence of the structure at its most abstract. each of these can go throug! the process shown in the figure generative process described earlier. Figure 2.11: The starting points for the generative design sequence (drawing after Durand). the process shown in the figure generative process described earlier.
numbers are used as abstractions to be used for mathematical operations in en gineering, geometry could be used for architecture Madrazo [1994]. Figure 2.1 below shows a plate with the title ‘Ensembles d’edifices resultants des division du quarre, du parallelogramme et de leurs cominaisons avec le cercle’ (plans re sulting from dissections of circle and square). This image shows diagrams only the essence of the structure at its most abstract. each of these can go throug! the process shown in the figure generative process described earlier. Figure 2.11: The starting points for the generative design sequence (drawing after Durand). the process shown in the figure generative process described earlier.
Figure 2.13: The transformation (through shear) from one species of fish to an- other. also influenced by this book in his own studies of morphogenesis ([Saunders, 1992, p.ix]) as were many of the architectural theorists of the 1970s including Mitchell, Steadman and March (Mitchell [1990]). The central theme of ‘On Growth and Form’ is that literature in the field of biology did not emphasise enough the role of physics and the growing process when describing the ‘form’ of an organism. This book addresses this problem by looking at the geometrical processes that give rise to form. Thus concepts such as allometry (the change in proportions with growth) were of central importance. Thompson also emphasised how simple transformations in the proportions could explain the difference between animals of the same body plan.
Figure 2.13: The transformation (through shear) from one species of fish to an- other. also influenced by this book in his own studies of morphogenesis ([Saunders, 1992, p.ix]) as were many of the architectural theorists of the 1970s including Mitchell, Steadman and March (Mitchell [1990]). The central theme of ‘On Growth and Form’ is that literature in the field of biology did not emphasise enough the role of physics and the growing process when describing the ‘form’ of an organism. This book addresses this problem by looking at the geometrical processes that give rise to form. Thus concepts such as allometry (the change in proportions with growth) were of central importance. Thompson also emphasised how simple transformations in the proportions could explain the difference between animals of the same body plan.
Figure 2.14: The comparison between jellyfish and ink drops.
Figure 2.14: The comparison between jellyfish and ink drops.
Figure 2.15: Diffusion through cells from ‘On Growth and Form’.
Figure 2.15: Diffusion through cells from ‘On Growth and Form’.
Figure 2.18: The topology for Frank Lloyd Wright drawing after Mitchell.
Figure 2.18: The topology for Frank Lloyd Wright drawing after Mitchell.
Figure 3.3: Framework for an evolutionary system by [Janssen, 2004, p.180].
Figure 3.3: Framework for an evolutionary system by [Janssen, 2004, p.180].
Figure 3.4: A review of modelling frameworks by John Frazer (unpublished).
Figure 3.4: A review of modelling frameworks by John Frazer (unpublished).
solver. The style sheet adds detail — windows, objects, doors — to the appear- ance(phenotype) of the solution. The solution having had it’s appearance altered can then be converted to a building information model. After the BIM model is made, further refinement is possible in a traditional BIM application. The evo- lutionary framework is not automating the entire design process but is assisting the exploration of many different solutions. Figure 3.6: The proposed workflow going from genetic instructions through to development and finally evaluation.
solver. The style sheet adds detail — windows, objects, doors — to the appear- ance(phenotype) of the solution. The solution having had it’s appearance altered can then be converted to a building information model. After the BIM model is made, further refinement is possible in a traditional BIM application. The evo- lutionary framework is not automating the entire design process but is assisting the exploration of many different solutions. Figure 3.6: The proposed workflow going from genetic instructions through to development and finally evaluation.
Figure 3.7: The isospatial grid in two dimensions
Figure 3.7: The isospatial grid in two dimensions
Figure 3.8: The set of 18 units used by the Reptile system.
Figure 3.8: The set of 18 units used by the Reptile system.
Figure 3.10 shows some trivial examples of L-system code being interpreted can only replace the left-side non-terminal with another single non-terminal, in context-free systems, any number of non-terminals and terminals are allowed on che right-hand side, in any order. One of the problems of the simplest machines hat accept regular grammars is that they have no explicit ‘memory’, they move rom one state to another. A machine that is allowed a certain amount of memory ‘a stack of memory) will now be used. L-systems use a rule-rewrite system which s then interpreted by a reader that reads relative coordinates. This is commonly called a ‘turtle’ and the drawings it produces are called ‘turtle-graphics’. There ire two parts to an L-system: an initial configuration, a rule set that describes che replacement of a symbol by another set. The turtle has a ‘memory stack’ and can remember a position in space and return to this position without drawing. There is a set of symbols that are read by the turtle in an L-System setup. In his section, only a small subset shall be used. These are:
Figure 3.10 shows some trivial examples of L-system code being interpreted can only replace the left-side non-terminal with another single non-terminal, in context-free systems, any number of non-terminals and terminals are allowed on che right-hand side, in any order. One of the problems of the simplest machines hat accept regular grammars is that they have no explicit ‘memory’, they move rom one state to another. A machine that is allowed a certain amount of memory ‘a stack of memory) will now be used. L-systems use a rule-rewrite system which s then interpreted by a reader that reads relative coordinates. This is commonly called a ‘turtle’ and the drawings it produces are called ‘turtle-graphics’. There ire two parts to an L-system: an initial configuration, a rule set that describes che replacement of a symbol by another set. The turtle has a ‘memory stack’ and can remember a position in space and return to this position without drawing. There is a set of symbols that are read by the turtle in an L-System setup. In his section, only a small subset shall be used. These are:
Figure 3.10: Turtle interpreting instructions.
Figure 3.10: Turtle interpreting instructions.
There is nothing in the structure of this system to prevent meaningless state- ments from forming. It should be recalled that in language, a similar remark was made by Chomsky who gave the famous line ‘Colourless green ideas sleep furiously’, a sentence that is grammatically correct, but has no semantic mean- ing. In the original Reptile article, a grid of ball bearings was used to represent a physical model of the structure, shown in Figure 3.13.This is shown in Figure 3. LO:
There is nothing in the structure of this system to prevent meaningless state- ments from forming. It should be recalled that in language, a similar remark was made by Chomsky who gave the famous line ‘Colourless green ideas sleep furiously’, a sentence that is grammatically correct, but has no semantic mean- ing. In the original Reptile article, a grid of ball bearings was used to represent a physical model of the structure, shown in Figure 3.13.This is shown in Figure 3. LO:
Figure 3.13: Ball bearings used to represent the Reptile structure Frazer [1974]
Figure 3.13: Ball bearings used to represent the Reptile structure Frazer [1974]
be placed onto in the same spot. Instead of the continous grid used in the previous representation, a discrete isospatial one shall now be used. On this grid, cells are placed on the integer coordinates of the grid. The turtle moves on this grid as it does in the representation used earlier, but instead of drawing shapes, it shall change the state of whatever cell its position coincides with. A growth sequence using the knot grid and the same rules used in the previous section is shown in Figure 3.14. The only difference is that instead of ’drawing’ the current (where the turtle is positioned) cell changes its color. Figure 3.14: The sequence grown from a knot seed over a discrete grid the turtle is positioned) cell changes its color.
be placed onto in the same spot. Instead of the continous grid used in the previous representation, a discrete isospatial one shall now be used. On this grid, cells are placed on the integer coordinates of the grid. The turtle moves on this grid as it does in the representation used earlier, but instead of drawing shapes, it shall change the state of whatever cell its position coincides with. A growth sequence using the knot grid and the same rules used in the previous section is shown in Figure 3.14. The only difference is that instead of ’drawing’ the current (where the turtle is positioned) cell changes its color. Figure 3.14: The sequence grown from a knot seed over a discrete grid the turtle is positioned) cell changes its color.
Figure 3.15: The rules used to make the Reptile structure shown on the right. eure 3.15, only the neighbours directly above need to be considered.
Figure 3.15: The rules used to make the Reptile structure shown on the right. eure 3.15, only the neighbours directly above need to be considered.
Figure 3.16: Truss system adapted from the base geometry of the ‘Reptile’ tiles. A pushdown automaton (the simplest machine that reads context-free gram- mars) could not read these instructions as it only has access to the top-most values in it’s stack, while there is a need to access any stored symbol at any point of the algorithms operation as well as ‘write-over’ existing values (i.e. step 5). These procedures require a very general computing machine. For a system that ‘evolves’, being able to change the procedures instead of hard-coding them would seem almost a prerequisite. As mentioned earlier one of the key aspects of using computer languages is the ability to keep building layers and more task specific languages on top of lower-level computational procedures.
Figure 3.16: Truss system adapted from the base geometry of the ‘Reptile’ tiles. A pushdown automaton (the simplest machine that reads context-free gram- mars) could not read these instructions as it only has access to the top-most values in it’s stack, while there is a need to access any stored symbol at any point of the algorithms operation as well as ‘write-over’ existing values (i.e. step 5). These procedures require a very general computing machine. For a system that ‘evolves’, being able to change the procedures instead of hard-coding them would seem almost a prerequisite. As mentioned earlier one of the key aspects of using computer languages is the ability to keep building layers and more task specific languages on top of lower-level computational procedures.
Figure 4.1: Instructions read by a processor Figure 4.1 shows a simple abstract automaton.
Figure 4.1: Instructions read by a processor Figure 4.1 shows a simple abstract automaton.
Table 4.1: The Chomsky Hierarchy of Language Grammars well. Each class of grammar within the Chomsky hierarchy contains the classes below them. Therefore, each is able to express a larger range of sentences than the ones below them. This generality however, comes at a price, otherwise there would be no reason not to use the most general class of grammar. The price paid is in the number of computational steps needed to read it and the complexity (and ambiguity) within the language.
Table 4.1: The Chomsky Hierarchy of Language Grammars well. Each class of grammar within the Chomsky hierarchy contains the classes below them. Therefore, each is able to express a larger range of sentences than the ones below them. This generality however, comes at a price, otherwise there would be no reason not to use the most general class of grammar. The price paid is in the number of computational steps needed to read it and the complexity (and ambiguity) within the language.
In a right-linear grammar, all the production rules have the terminal symbol preceding the non-terminal. In a left-linear grammar, they succeed the non- terminal. Regular anguages are languages that can be generated from regular grammars. A regular expression is a formal way of expressing rules for matching patterns of strings rom these regular languages. The compact nature of regular expressions make t hem a very convenient way to express patterns of symbol se- quences. Four important conventions that are used within regular expressions in computer science are shown in the next table. Thus each takes the generic forms for a single grammar shown below.
In a right-linear grammar, all the production rules have the terminal symbol preceding the non-terminal. In a left-linear grammar, they succeed the non- terminal. Regular anguages are languages that can be generated from regular grammars. A regular expression is a formal way of expressing rules for matching patterns of strings rom these regular languages. The compact nature of regular expressions make t hem a very convenient way to express patterns of symbol se- quences. Four important conventions that are used within regular expressions in computer science are shown in the next table. Thus each takes the generic forms for a single grammar shown below.
Figure 4.2: A transition diagram showing a set of possible descriptions for a house. here to the ability to create more complex constructs from a set of elementary units (or granules). This might also considered to be a ‘domain specific language’ though perha ps too simple to be of any use. Figure 4.2 can be understood as an abstract machine, one that has a finite number of states. Each state is a word or group of words from this language and the transitions between them control the order in which they can be joined.
Figure 4.2: A transition diagram showing a set of possible descriptions for a house. here to the ability to create more complex constructs from a set of elementary units (or granules). This might also considered to be a ‘domain specific language’ though perha ps too simple to be of any use. Figure 4.2 can be understood as an abstract machine, one that has a finite number of states. Each state is a word or group of words from this language and the transitions between them control the order in which they can be joined.
The strength of this representation lies in its conciseness, while its weakness
The strength of this representation lies in its conciseness, while its weakness
Figure 4.5: Diagrams used to describe finite machines.
Figure 4.5: Diagrams used to describe finite machines.
Some of these will play a larger role in the next chapter. is by looking at how much control they have over the way rewriting takes place.
Some of these will play a larger role in the next chapter. is by looking at how much control they have over the way rewriting takes place.
Figure 4.7: A family of columns (Frazer [1995]). The list may consist of integers, real numbers or an element from an enu merated list (such as roof type). Many proprietary scripting languages allow th building of parameterised models, where the values can be altered for differen instances of the model. One of the most well-known of these is the GDL scrip that was created by Graphisoft for their commercial software ArchiCAD. As a: example of a very simple parameter-driven architectural model, consider a simpl rectangular building, with the parameters of length, width, and orientation. Th
Figure 4.7: A family of columns (Frazer [1995]). The list may consist of integers, real numbers or an element from an enu merated list (such as roof type). Many proprietary scripting languages allow th building of parameterised models, where the values can be altered for differen instances of the model. One of the most well-known of these is the GDL scrip that was created by Graphisoft for their commercial software ArchiCAD. As a: example of a very simple parameter-driven architectural model, consider a simpl rectangular building, with the parameters of length, width, and orientation. Th
Figure 4.8: An elementary example of a parameterized model. uses the other parameters to position and lengthen the beams. values used to create instances of this parameterised model would be a list of three real numbers. A script that accepts these numbers in turn and uses them to build a simple shed could be defined with an algorithm that reads the length and places beams at an even spacing along one of the axes of the building and uses the other parameters to position and lengthen the beams.
Figure 4.8: An elementary example of a parameterized model. uses the other parameters to position and lengthen the beams. values used to create instances of this parameterised model would be a list of three real numbers. A script that accepts these numbers in turn and uses them to build a simple shed could be defined with an algorithm that reads the length and places beams at an even spacing along one of the axes of the building and uses the other parameters to position and lengthen the beams.
Figure 4.9: Simple buildings from printed from two different inputs. turn have the printer print out the forms shown in Figure 4.9. The smallest string that can be produced with this grammar is three symbols long which would cause the printer to produce a one storey building of one of the three base profiles given. The grammar also ensures that the symbol which governs the base profile can only be used once in any sentence. In this case, the size of the input string is not fixed, though its structure can be described as linear. Examples of valid strings would be {swfwr}, {sfwfwfwr} which would in turn have the printer print out the forms shown in Figure 4.9.
Figure 4.9: Simple buildings from printed from two different inputs. turn have the printer print out the forms shown in Figure 4.9. The smallest string that can be produced with this grammar is three symbols long which would cause the printer to produce a one storey building of one of the three base profiles given. The grammar also ensures that the symbol which governs the base profile can only be used once in any sentence. In this case, the size of the input string is not fixed, though its structure can be described as linear. Examples of valid strings would be {swfwr}, {sfwfwfwr} which would in turn have the printer print out the forms shown in Figure 4.9.
Figure 4.10: Drawing after Bemis and Burchard [1938].
Figure 4.10: Drawing after Bemis and Burchard [1938].
The dissection sequence is shown in Figure 4.12 Figure 4.12: A set of rectangular dissections. With this system, the tokens that are at the left end of the string create more of an impact than the ones at the right end. In this system, the order of the dis- section operations alters the final form generated. With systems that are based on serial processes where the order of operations has large qualitative changes. there is the danger that a small mutation at the wrong position leads to a very big change in the final form or the solution will become invalid. This makes them inappropriate for evolutionary modelling which favours gradual development tc find optima. Another limitation of dissecting rectangles is that certain configu- rations cannot be produced. This as noted by | shown in Figure 4.13 on the left. Farl [1977] who gave the example
The dissection sequence is shown in Figure 4.12 Figure 4.12: A set of rectangular dissections. With this system, the tokens that are at the left end of the string create more of an impact than the ones at the right end. In this system, the order of the dis- section operations alters the final form generated. With systems that are based on serial processes where the order of operations has large qualitative changes. there is the danger that a small mutation at the wrong position leads to a very big change in the final form or the solution will become invalid. This makes them inappropriate for evolutionary modelling which favours gradual development tc find optima. Another limitation of dissecting rectangles is that certain configu- rations cannot be produced. This as noted by | shown in Figure 4.13 on the left. Farl [1977] who gave the example
Figure 4.13: An outcome that cannot be accomplished with dissection alone and a plan that might use this configuration after March and Steadman [1971].
Figure 4.13: An outcome that cannot be accomplished with dissection alone and a plan that might use this configuration after March and Steadman [1971].
the Palladian Villa set that has been encountered in the literature review could be represented as 4.15. Figure 4.15: The Villa Malcontenta with a GP-System.
the Palladian Villa set that has been encountered in the literature review could be represented as 4.15. Figure 4.15: The Villa Malcontenta with a GP-System.
Figure 4.14: Various shapes possible with GP-systems.
Figure 4.14: Various shapes possible with GP-systems.
Figure 4.17: A run of a simulation using GP systems, areas shaded show identical solutions due to naive selection process.
Figure 4.17: A run of a simulation using GP systems, areas shaded show identical solutions due to naive selection process.
Figure 4.18: The kernel as a set of rules and starting position. .l Definition and Conventions
Figure 4.18: The kernel as a set of rules and starting position. .l Definition and Conventions
Table 4.2: Examples of evolutionary design experiments. Usually approaches to evolutionary modelling that use context-free languages will be based on genetic programming as opposed to genetic algorithms. A good source for the computational side to genetic programming as used in this explo- ration can be gathered from Koza [1990]. Design cases that uses nested represen- tations have a tendency to be more conceptual and abstract than the examples mentioned in the previous section (such as the work of Janssen).
Table 4.2: Examples of evolutionary design experiments. Usually approaches to evolutionary modelling that use context-free languages will be based on genetic programming as opposed to genetic algorithms. A good source for the computational side to genetic programming as used in this explo- ration can be gathered from Koza [1990]. Design cases that uses nested represen- tations have a tendency to be more conceptual and abstract than the examples mentioned in the previous section (such as the work of Janssen).
Figure 4.19: Rectangles overlaid on the grid. 4.4.3.2 Composing plans One of the major advantages of using GL-Systems is that many compositional motifs can be described. In the case of Palladian Villas, a compositional feature might be that of bilateral symmetry. As previously stated, it is better that compositional patterns not be hard-coded into the algorithmic side of the process as the system would then never be able to lose or gain those traits during their evolution. Some compositional themes (Linearity, bilateral symmetry and radial symmetry) used will now be represented with L-system rules. Linearity can be ached simply by making the turtle move forward with the symbol ‘F’.
Figure 4.19: Rectangles overlaid on the grid. 4.4.3.2 Composing plans One of the major advantages of using GL-Systems is that many compositional motifs can be described. In the case of Palladian Villas, a compositional feature might be that of bilateral symmetry. As previously stated, it is better that compositional patterns not be hard-coded into the algorithmic side of the process as the system would then never be able to lose or gain those traits during their evolution. Some compositional themes (Linearity, bilateral symmetry and radial symmetry) used will now be represented with L-system rules. Linearity can be ached simply by making the turtle move forward with the symbol ‘F’.
Figure 4.20: Palladio’s Villa Cornaro approximated with a GL-System.
Figure 4.20: Palladio’s Villa Cornaro approximated with a GL-System.
Figure 4.23: Combination of two motifs. Figure 4.22: Elements spread out to show the axes.
Figure 4.23: Combination of two motifs. Figure 4.22: Elements spread out to show the axes.
‘his creates the tree structure similar to the one shown in the Reptiles exam. ple. A recursive tree structure is created by inserting ‘A’ into the right-side of the rule. Growth can be used to group designs of similar compositional themes by comparing different iterations of the same code. Figure 4.24 shows two iteration: of a GL system. The two have the same kernel but are simply at two different stages of growth. This representation allows for these two to be connected anc be situated within the same family which was not possible in the representation: used with GP-Systems. Figure 4.24: A GL representation of a Villa’s growth after two and three itera- tions.
‘his creates the tree structure similar to the one shown in the Reptiles exam. ple. A recursive tree structure is created by inserting ‘A’ into the right-side of the rule. Growth can be used to group designs of similar compositional themes by comparing different iterations of the same code. Figure 4.24 shows two iteration: of a GL system. The two have the same kernel but are simply at two different stages of growth. This representation allows for these two to be connected anc be situated within the same family which was not possible in the representation: used with GP-Systems. Figure 4.24: A GL representation of a Villa’s growth after two and three itera- tions.
Figure 4.25: A tree representation of the equation (8+2)*4 and of the GL-code ‘FF|[+F][-F]’ as a n-ary and binary tree.
Figure 4.25: A tree representation of the equation (8+2)*4 and of the GL-code ‘FF|[+F][-F]’ as a n-ary and binary tree.
Figure 4.26: A recombination operation on a rewrite rule. Unlike the species present in biology where the body-plan remains the same, with spatial design, the interest is in topological change. How to keep population members as emerging from the same family while having them being topologically different comes as a challenge. In the case of the villas, this was done by using
Figure 4.26: A recombination operation on a rewrite rule. Unlike the species present in biology where the body-plan remains the same, with spatial design, the interest is in topological change. How to keep population members as emerging from the same family while having them being topologically different comes as a challenge. In the case of the villas, this was done by using
Figure 4.27: A model representation where the rules can make references to the environment.
Figure 4.27: A model representation where the rules can make references to the environment.
Figure 4.28: An example of a design model that uses a context-sensitive grammat drawn after Wojtowicz and Fawcett [1986].
Figure 4.28: An example of a design model that uses a context-sensitive grammat drawn after Wojtowicz and Fawcett [1986].
Table 4.3: Examples of design experiments using cellular automata. automata such as the examples in Table 4.3
Table 4.3: Examples of design experiments using cellular automata. automata such as the examples in Table 4.3
Figure 4.29: Some room configurations. To represent the problem, the grid notation used in the section on regular
Figure 4.29: Some room configurations. To represent the problem, the grid notation used in the section on regular
Figure 4.30: Room divided into grid and cells on perimeter have been tagged to a different state.
Figure 4.30: Room divided into grid and cells on perimeter have been tagged to a different state.
Figure 4.31: The gradients of cell states for each element channel.
Figure 4.31: The gradients of cell states for each element channel.
Figure 4.32: Furniture elements represented with cells.
Figure 4.32: Furniture elements represented with cells.
Figure 4.33: The behaviour of each ‘furniture cell’.
Figure 4.33: The behaviour of each ‘furniture cell’.
Figure 4.34: The movement of a furniture cell. Figure 4.35: Furniture elements.
Figure 4.34: The movement of a furniture cell. Figure 4.35: Furniture elements.
Figure 4.36: An example of a good solution to the requirements.
Figure 4.36: An example of a good solution to the requirements.
Figure 4.37: A general processor reading a general kernel. Unrestricted grammars (Type-0) are the most general class on the Chomsky Hierarchy. They define languages which are referred to as recursively-enumerable. The most interesting aspect of this class grammar is the relationship it has with computation. Type-0 grammar production rules are defined as:
Figure 4.37: A general processor reading a general kernel. Unrestricted grammars (Type-0) are the most general class on the Chomsky Hierarchy. They define languages which are referred to as recursively-enumerable. The most interesting aspect of this class grammar is the relationship it has with computation. Type-0 grammar production rules are defined as:
The equivalent action by a Turing machine is shown in Figure 4.39. Figure 4.39: A Turing machine adding one to binary string.
The equivalent action by a Turing machine is shown in Figure 4.39. Figure 4.39: A Turing machine adding one to binary string.
are easier to notate than that of an unrestricted grammar as the right hand side need only have 3 symbols. The major difference is that the initial state would need to given in a separate notation, unlike GL-Systems where the initial state could be given as a production rule. One notation that could be used to give Turing machine instruction within GL code is to separate the two sections, in this case with an & symbol and to have the control rules in a similar form to the rewrite rules used previously but with two left-hand symbols, one to show the state and what symbol the tape head is reading. An example of this (taken from the first two rules of the counting Turing machine) is 101&Q1,0: Q1,0, R; Q1,0: Q1,1,R;. rules of the counting Turing machine) is 101&Q1,0: Q1,0, R; Q1,0: @Q1,1,R;. Figure 4.40: A Turing machine copying a string.
are easier to notate than that of an unrestricted grammar as the right hand side need only have 3 symbols. The major difference is that the initial state would need to given in a separate notation, unlike GL-Systems where the initial state could be given as a production rule. One notation that could be used to give Turing machine instruction within GL code is to separate the two sections, in this case with an & symbol and to have the control rules in a similar form to the rewrite rules used previously but with two left-hand symbols, one to show the state and what symbol the tape head is reading. An example of this (taken from the first two rules of the counting Turing machine) is 101&Q1,0: Q1,0, R; Q1,0: Q1,1,R;. rules of the counting Turing machine) is 101&Q1,0: Q1,0, R; Q1,0: @Q1,1,R;. Figure 4.40: A Turing machine copying a string.
Figure 4.41: A universal Turing machine after Denning et al. [1978]
Figure 4.41: A universal Turing machine after Denning et al. [1978]
Table 5.1: The subsystems presented by Miller in Living Systems (Miller [1978]).
Table 5.1: The subsystems presented by Miller in Living Systems (Miller [1978]).
species that remains stable and a perturbation from this decays to zero. Figure 5.1: The population of two species, predators and prey modelled as a Lotka-Volterra System.
species that remains stable and a perturbation from this decays to zero. Figure 5.1: The population of two species, predators and prey modelled as a Lotka-Volterra System.
Figure 5.2: The two chemical (activator and inhibitor) alter each other’s produc- tion rates and diffuse to adjacent cells. pattern formations have been found, for example Meinhardt [1995] describes the
Figure 5.2: The two chemical (activator and inhibitor) alter each other’s produc- tion rates and diffuse to adjacent cells. pattern formations have been found, for example Meinhardt [1995] describes the
Table 5.2: Diffusion simulated with a cellular automaton.
Table 5.2: Diffusion simulated with a cellular automaton.
Table 5.3: Results of a reaction-diffusion simulation with two different reaction functions.
Table 5.3: Results of a reaction-diffusion simulation with two different reaction functions.
Figure 5.3: The similarities between the Villa Stein and Villa Malcontenta, first described by Rowe [1982]. show a greater amount of asymmetry than the architecture preceding them. This can be seen as a natural evolutionary In the GL-system code that was used instruct the Turtle to reverse its direc step, if the biological metaphor is applied. in Chapter 3, the symbol ‘|’ was used to tion and mirror its movements for turning. The problem with representing genoty pes this way (or with the palindrome gram- mar) is that this symbol is followed rigidly, with no chance of it ever deviating from creating an exact mirror. It is desirable that the plans stay symmetrical for a large period of the evolutionary process and only after a lengthy period, lose their symmetry.
Figure 5.3: The similarities between the Villa Stein and Villa Malcontenta, first described by Rowe [1982]. show a greater amount of asymmetry than the architecture preceding them. This can be seen as a natural evolutionary In the GL-system code that was used instruct the Turtle to reverse its direc step, if the biological metaphor is applied. in Chapter 3, the symbol ‘|’ was used to tion and mirror its movements for turning. The problem with representing genoty pes this way (or with the palindrome gram- mar) is that this symbol is followed rigidly, with no chance of it ever deviating from creating an exact mirror. It is desirable that the plans stay symmetrical for a large period of the evolutionary process and only after a lengthy period, lose their symmetry.
Figure 5.4: Pask’s diagrams for coupling between two subsystems (Pask [1969]). One of the key inspirations for the ML-Systems representation comes from Pask [1969] and is shown in Figure 5.4. This diagram shows a coupling between t nN wo systems. In the first, the output from one subsystem is transferred to the next. This type of connection is typical of many visual programming languages. The second diagram however shows a subsystem affecting the parameters of another. n This type of connection forms the basis of exploration to follow. This exploration will make use of diagrams over the textual representations used in the last chapter. vill make use of diagrams over the textual representations used in the last chapter.
Figure 5.4: Pask’s diagrams for coupling between two subsystems (Pask [1969]). One of the key inspirations for the ML-Systems representation comes from Pask [1969] and is shown in Figure 5.4. This diagram shows a coupling between t nN wo systems. In the first, the output from one subsystem is transferred to the next. This type of connection is typical of many visual programming languages. The second diagram however shows a subsystem affecting the parameters of another. n This type of connection forms the basis of exploration to follow. This exploration will make use of diagrams over the textual representations used in the last chapter. vill make use of diagrams over the textual representations used in the last chapter.
Figure 5.5: The base subsystem from which all the other subsystems arise from.
Figure 5.5: The base subsystem from which all the other subsystems arise from.
Figure 5.6: Diffusion of morphogen ‘a’ through the system and subsystem arriving after threshold is reached. io 4
Figure 5.6: Diffusion of morphogen ‘a’ through the system and subsystem arriving after threshold is reached. io 4
Figure 5.7: Multiple environment cells overlaid
Figure 5.7: Multiple environment cells overlaid
Figure 5.8: A motor subsystem responding to different signals. the ‘processing’ or ‘computing’ unit in that it is needed to give decodes messages and instructs movement in the other subsystems. In biology, ‘cell signaling’ is a complex interaction between cells that coordinate various biological actions. Some important aspects of this are that cells signals can be amplified and that the same signal can cause different physiological response in different cells. ‘Am- plification’ means that a small signal can create a large reaction. Abstracting from this biological metaphor, a system can be designed where ‘signals’ are sent between entities. Instead of the physical shape of the receptor cell which aligns itself to the signaling molecule, a number code can be used which representing what signaling actions correspond to what entities.
Figure 5.8: A motor subsystem responding to different signals. the ‘processing’ or ‘computing’ unit in that it is needed to give decodes messages and instructs movement in the other subsystems. In biology, ‘cell signaling’ is a complex interaction between cells that coordinate various biological actions. Some important aspects of this are that cells signals can be amplified and that the same signal can cause different physiological response in different cells. ‘Am- plification’ means that a small signal can create a large reaction. Abstracting from this biological metaphor, a system can be designed where ‘signals’ are sent between entities. Instead of the physical shape of the receptor cell which aligns itself to the signaling molecule, a number code can be used which representing what signaling actions correspond to what entities.
Figure 5.9: Different types of the signaler subsystem.
Figure 5.9: Different types of the signaler subsystem.
Figure 5.10: A ring of signaler cells used to create a 1D reaction-diffusion system VY A group of signaler cells can be connected together to form turn, create a Reaction-Diffusion system. As the chemicals are a a 1D ring an in ready diffusing all that is need to to have the reaction turn which can be given with a simple expression: The effect of this, is by varying the constants in t he formula, the number of peaks can be altered and this could act as a mechanism to give in- structions to another subsystem, for example, a motor. The num ber of ‘peaks’ in a RD-System is relatively constant, given the same number of cells in the ring. Regardless of small noise at the start, the systems moves toward that has the same number of peaks. s a distribution that has the same number of peaks.
Figure 5.10: A ring of signaler cells used to create a 1D reaction-diffusion system VY A group of signaler cells can be connected together to form turn, create a Reaction-Diffusion system. As the chemicals are a a 1D ring an in ready diffusing all that is need to to have the reaction turn which can be given with a simple expression: The effect of this, is by varying the constants in t he formula, the number of peaks can be altered and this could act as a mechanism to give in- structions to another subsystem, for example, a motor. The num ber of ‘peaks’ in a RD-System is relatively constant, given the same number of cells in the ring. Regardless of small noise at the start, the systems moves toward that has the same number of peaks. s a distribution that has the same number of peaks.
Figure 5.11: A set of nested boundary subsystems each dissolving at a different threshold of morphogen ‘a’.
Figure 5.11: A set of nested boundary subsystems each dissolving at a different threshold of morphogen ‘a’.
Frank Lloyd Wright’s Martin House will be worked through to illustrate the key aspects of ML-Systems. Instead of evolving designs out for a desired spatia adjacency, the form of Martin house will be analysed with ML-Systems. First the form of the house is simplified and abstracted so that the essential component: are highlighted. Figure 5.12 shows the main compositional features of the house are highlighted. Figure 5.12 shows the main compositional features of the house. An ‘origin’ for this house is needed. Laseau and Tice [1992] writes about the similarities of Wright’s prairie style to the villas of Palladio. A simple cross (from Durand’s starting forms) can be taken as a starting point and this can be used to relate Wright’s Prairie houses to their ancestors which in this narrative are Palladian Villas. The next step is in finding the major axis that extend from this simple form. The minor axes can then be mapped and how the spaces branch of them are mapped. The traversal axes is elongated and shall become the primary
Frank Lloyd Wright’s Martin House will be worked through to illustrate the key aspects of ML-Systems. Instead of evolving designs out for a desired spatia adjacency, the form of Martin house will be analysed with ML-Systems. First the form of the house is simplified and abstracted so that the essential component: are highlighted. Figure 5.12 shows the main compositional features of the house are highlighted. Figure 5.12 shows the main compositional features of the house. An ‘origin’ for this house is needed. Laseau and Tice [1992] writes about the similarities of Wright’s prairie style to the villas of Palladio. A simple cross (from Durand’s starting forms) can be taken as a starting point and this can be used to relate Wright’s Prairie houses to their ancestors which in this narrative are Palladian Villas. The next step is in finding the major axis that extend from this simple form. The minor axes can then be mapped and how the spaces branch of them are mapped. The traversal axes is elongated and shall become the primary
Figure 5.15: Formation of secondary boundary shapes.
Figure 5.15: Formation of secondary boundary shapes.
eventually dissolves to release the inner boundaries to the environment.
eventually dissolves to release the inner boundaries to the environment.
Figure 5.17: Adjacencies are calculated this is used to create feedback loops between subsystems.
Figure 5.17: Adjacencies are calculated this is used to create feedback loops between subsystems.
Figure 6.1: A diagram of the ‘Tree of Life’ (Letunic [2008])
Figure 6.1: A diagram of the ‘Tree of Life’ (Letunic [2008])
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