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Creative Systems as Dynamical Systems

Alessandro Valitutti
Alessandro Valitutti

we discuss ideas for characterizing a case- based generative system as creative. Focusing on a specific generator of graphics, we performed a qualitative exploration of the space of solu- tions. The emerged intuition is that the set of configurations generated by the program can be viewed both as the conceptual space of a creative system and the phase space of a dynamical system. In the context of this analogy, we hypothesize that a higher degree of creativity can be ascribed to the search paths allowing the system to reach new basins of attractions.

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Creative Systems as Dynamical Systems Alessandro 油Valitutti 油 University 油College 油Dublin 油 ICCBR-足15 油 28 油September 油2015 油
Rationale ≒ A 油conceptual 油space 油of 油a 油creative 油system 油can 油be 油 decomposed 油in 油several 油regions 油called 油basins 油of 油 attractions, 油each 油associated 油to 油a 油speci鍖c 油type 油of 油 artefacts. 油 ≒ Classic 油CBR 油is 油conservative, 油i.e. 油generates 油solutions 油 included 油in 油the 油basin 油of 油attraction 油containing 油the 油past 油 examples. 油 ≒ We 油propose 油two 油forms 油of 油similarity 油between 油artefacts, 油 according 油to 油typicality 油(t-足similarity) 油and 油value 油(v-足 similarity). 油Their 油combined 油use 油allows 油CBR 油to 油reach 油 di鍖erent 油basins 油of 油attractions 油and 油makes 油it 油more 油creative. 油 1 油ICCBR-足15 油 28 油September 油2015 油
Outline 1. Creative 油Systems 油 2. The 油Fractal 油Tree 油 3. Analogies 油 4. Key 油Ideas 油 2 油ICCBR-足15 油 28 油September 油2015 油
Creative Systems (Wiggins 油2006): 油 ≒ The 油conceptual 油space 油is 油a 油set 油of 油artefacts 油(in 油 Bodens 油terms, 油concepts) 油which 油are 油in 油some 油 quasi-足syntactic 油sense 油deemed 油to 油be 油acceptable 油 as 油examples 油of 油whatever 油is 油being 油created. 油 Implicitly, 油the 油conceptual 油space 油may 油include 油 partially 油de鍖ned 油artefacts 油too. 油 ≒ Exploratory 油creativity 油is 油the 油process 油of 油 exploring 油a 油given 油conceptual 油space 油 油 3 油ICCBR-足15 油 28 油September 油2015 油
Creative Systems (Wiggins 油2006): 油 A 油creative 油system 油is 油represented 油by 油the 油following 油symbols: 油 ≒ L 油is 油a 油language 油in 油which 油to 油express 油concepts 油(artefacts) 油and 油rules ≒ U 油is 油the 油(abstract) 油set 油of 油all 油possible 油partial 油and 油complete 油artefacts 油describable 油in 油 the 油creative 油system 油being 油modelled 油 ≒ T 油is 油a 油set 油of 油rules 油which 油[...] 油describe 油the 油behaviour 油of 油a 油creative 油agent 油as 油it 油 traverses 油the 油conceptual 油space 油from 油known 油artefacts 油to 油unknown 油ones 油[...] 油and 油 possibly 油back 油again 油 ≒ R 油is 油a 油set 油of 油rules, 油expressed 油using 油the 油language 油L, 油which 油select 油an 油acceptable 油or 油 relevant 油subset 油of 油U 油which 油corresponds 油with 油Bodens1 油conceptual 油space 油 油 ≒ is 油a 油set 油of 油rules 油by 油which 油value 油is 油attributed 油to 油a 油created 油artefact 油 油 4 油ICCBR-足15 油 28 油September 油2015 油
Creative Systems 5 油ICCBR-足15 油 28 油September 油2015 油 (Ritchie 油2007): 油 ≒ set 油of 油basic 油items 油B 油= 油data 油types 油(e.g. 油string 油of 油words, 油arrays 油of 油pixels) 油 characterising 油the 油artefacts 油produced 油by 油the 油program 油 ≒ set 油of 油results 油R 油= 油set 油of 油artefacts 油produced 油by 油the 油program 油with 油a 油 speci鍖c 油set 油of 油setting 油parameters 油 ≒ inspiring 油set 油I: 油The 油construction 油of 油the 油program 油is 油in鍖uenced 油(either 油 explicitly 油or 油implicitly) 油by 油some 油subset 油of 油the 油available 油basic 油items. 油This 油 subset, 油which 油we 油will 油call 油the 油inspiring 油set, 油could 油be 油all 油the 油relevant 油 artefacts 油known 油to 油the 油program 油designer, 油or 油items 油which 油the 油 program 油is 油designed 油to 油replicate, 油or 油a 油knowledge 油base 油of 油known 油 examples 油which 油drives 油the 油computation 油within 油the 油program. 油 油
Creative Systems 6 油ICCBR-足15 油 28 油September 油2015 油 (Ritchie 油2007): 油 ≒ typ(X) 油= 油value 油of 油typicality 油associated 油to 油the 油 artefact 油X 油 ≒ val(X) 油= 油value 油of 油quality 油associated 油to 油X 油 ≒ T留,硫(X) 油= 油{x 油 油X 油| 油留 油 油typ(X) 油 油硫} 油 ≒ V留,硫(X) 油= 油{x 油 油X 油| 油留 油 油val(X) 油 油硫} 油
B Set 油of 油basic 油items 油
B I 油 Inspiring 油set 油
B I 油 Set 油of 油results 油 R
B I 油 R Typical 油artefacts 油 T留,1(R) 油= 油{x 油 油R 油| 油留 油 油typ(X) 油 油1} 油 T留,1(R) 油
B I 油 R Valuable 油artefacts 油 V粒,1(R) 油= 油{x 油 油R 油| 油粒 油 油val(X) 油 油1} 油 V粒,1(R) 油
The Fractal Tree 12 油ICCBR-足15 油 28 油September 油2015 油
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Observations 油 ≒ Shape 油types: 油polygon, 油snow 油鍖ake, 油vegetable 油 ≒ Shape 油dimensions: 油curvature, 油aperture, 油 symmetry 油 ≒ Optimal 油con鍖gurations 油 28 油September 油2015 油ICCBR-足15 油 36 油
Main Analogies Creative 油System 油 37 油ICCBR-足15 油 28 油September 油2015 油 Problem 油Solver 油 Dynamical 油System 油
Creative System as Dynamical System What 油is 油a 油path 油in 油the 油square 油of 油fractal 油trees? 油 1. A 油search 油in 油the 油conceptual 油space 油of 油a 油creative 油system 油 2. A 油trajectory 油in 油the 油phase 油space 油of 油a 油dynamical 油system 油 An 油attractor 油is 油a 油set 油of 油states 油(i.e., 油elements 油of 油the 油state 油 space 油of 油a 油dynamical 油system) 油towards 油which 油a 油set 油of 油 dynamical 油paths 油tend 油to 油evolve. 油 The 油set 油of 油dynamical 油paths 油pointing 油to 油the 油attractor 油is 油 called 油basin 油of 油attraction. 油 38 油ICCBR-足15 油 28 油September 油2015 油
Basin Jumping and Creativity ≒ The 油conceptual 油space 油can 油be 油decomposed 油in 油basins 油of 油attraction. 油 油 ≒ Starting 油from 油a 油set 油of 油past 油examples 油(inspiration 油set), 油a 油creative 油system 油 can 油reach 油 油from 油which 油a 油speci鍖c 油basin 油of 油attraction 油can 油be 油explored. 油 ≒ Classic 油CBR 油allows 油a 油creative 油system 油to 油explore 油the 油basin 油of 油 attraction 油containing 油the 油set 油of 油past 油examples 油(assumed 油to 油be 油the 油 inspiration 油set) 油 ≒ Creative 油CBR 油should 油allows 油a 油creative 油system 油to 油reach 油basin 油of 油 attractions 油not 油containing 油the 油past 油examples 油 ≒ In 油summary, 油if 油we 油assume 油the 油creativity 油as 油a 油search 油in 油the 油conceptual 油 space, 油a 油higher 油degree 油of 油creativity 油is 油associated 油to 油the 油search 油of 油new 油 basins 油of 油attraction 油(basin 油jumping). 油 油 39 油ICCBR-足15 油 28 油September 油2015 油
Double Similarity ≒ CBR 油is 油based 油on 油the 油capability 油to 油recognize 油a 油new 油case 油as 油 similar 油to 油one 油of 油the 油past 油cases 油 ≒ Creative 油CBR 油should 油employ 油two 油forms 油of 油similarity: 油 ≒ T-足Similarity: 油degree 油to 油which 油two 油artefacts 油are 油recognised 油as 油 belonging 油to 油the 油same 油type 油 ≒ V-足Similarity: 油degree 油to 油which 油the 油value 油of 油two 油artefacts 油is 油 recognised 油as 油similar 油 ≒ T-足similarity 油allows 油the 油system 油to 油explore 油the 油current 油basin 油 of 油attraction 油 ≒ V-足similarity 油allows 油the 油system 油to 油reach 油di鍖erent 油basins 油of 油 attraction 油 40 油ICCBR-足15 油 28 油September 油2015 油
Types of Attraction Basins ≒ Types 油of 油artefacts 油 ≒ Creative 油Ideation: 油di鍖erent 油renderings 油of 油the 油 same 油idea 油 ≒ Components 油of 油an 油artefact 油(e.g. 油lexical 油 component 油of 油a 油text) 油 ≒ Di鍖erent 油styles 油or 油patterns 油 41 油ICCBR-足15 油 28 油September 油2015 油
Summary of Key Ideas ≒ Analogies 油 ≒ problem 油solving: 油state/search 油space 油 ≒ generative 油system: 油space 油of 油con鍖guration 油 ≒ creative 油system: 油conceptual 油space 油 ≒ dynamical 油system: 油phase 油space 油 ≒ CBR: 油past 油examples, 油inspiring 油set 油and 油basin 油of 油 attraction 油 ≒ Multiplicity 油of 油attraction 油basins 油 ≒ Double 油similarity 油and 油basin 油jumping 油 42 油ICCBR-足15 油 28 油September 油2015 油
Future Work ≒ Exploiting 油creative 油systems 油complexity 油(Typ 油vs. 油 Val, 油truth 油inference 油vs. 油valence 油inference) 油 ≒ Application 油to 油鍖ctional 油ideation: 油di鍖erent 油 renderings 油of 油the 油same 油idea 油 ≒ Application 油to 油linguistic 油creativity: 油 parametrisation 油and 油connection 油of 油di鍖erent 油 patterns 油 43 油ICCBR-足15 油 28 油September 油2015 油
References ≒ G. 油Wiggins 油(2006). 油Searching 油for 油Computational 油 Creativity. 油New 油Generation 油Computing, 油24(3). 油 ≒ G. 油Ritchie 油(2007). 油Some 油Empirical 油Criteria 油for 油 Attributing 油Creativity 油to 油a 油Computer 油Program. 油 Minds 油and 油Machines, 油17(1). 油 ≒ R. 油Gibbs 油(2012). 油Metaphors, 油snow鍖akes, 油and 油 termite 油nests. 油How 油nature 油creates 油such 油beautiful 油 things. 油Chapter 油published 油in: 油Metaphor 油in 油Use: 油 Context, 油culture, 油and 油communication. 油 油Amsterdam: 油 John 油Benjamins. 油 44 油ICCBR-足15 油 28 油September 油2015 油

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Creative Systems as Dynamical Systems

  • 1. Creative Systems as Dynamical Systems Alessandro 油Valitutti 油 University 油College 油Dublin 油 ICCBR-足15 油 28 油September 油2015 油
  • 2. Rationale ≒ A 油conceptual 油space 油of 油a 油creative 油system 油can 油be 油 decomposed 油in 油several 油regions 油called 油basins 油of 油 attractions, 油each 油associated 油to 油a 油speci鍖c 油type 油of 油 artefacts. 油 ≒ Classic 油CBR 油is 油conservative, 油i.e. 油generates 油solutions 油 included 油in 油the 油basin 油of 油attraction 油containing 油the 油past 油 examples. 油 ≒ We 油propose 油two 油forms 油of 油similarity 油between 油artefacts, 油 according 油to 油typicality 油(t-足similarity) 油and 油value 油(v-足 similarity). 油Their 油combined 油use 油allows 油CBR 油to 油reach 油 di鍖erent 油basins 油of 油attractions 油and 油makes 油it 油more 油creative. 油 1 油ICCBR-足15 油 28 油September 油2015 油
  • 3. Outline 1. Creative 油Systems 油 2. The 油Fractal 油Tree 油 3. Analogies 油 4. Key 油Ideas 油 2 油ICCBR-足15 油 28 油September 油2015 油
  • 4. Creative Systems (Wiggins 油2006): 油 ≒ The 油conceptual 油space 油is 油a 油set 油of 油artefacts 油(in 油 Bodens 油terms, 油concepts) 油which 油are 油in 油some 油 quasi-足syntactic 油sense 油deemed 油to 油be 油acceptable 油 as 油examples 油of 油whatever 油is 油being 油created. 油 Implicitly, 油the 油conceptual 油space 油may 油include 油 partially 油de鍖ned 油artefacts 油too. 油 ≒ Exploratory 油creativity 油is 油the 油process 油of 油 exploring 油a 油given 油conceptual 油space 油 油 3 油ICCBR-足15 油 28 油September 油2015 油
  • 5. Creative Systems (Wiggins 油2006): 油 A 油creative 油system 油is 油represented 油by 油the 油following 油symbols: 油 ≒ L 油is 油a 油language 油in 油which 油to 油express 油concepts 油(artefacts) 油and 油rules ≒ U 油is 油the 油(abstract) 油set 油of 油all 油possible 油partial 油and 油complete 油artefacts 油describable 油in 油 the 油creative 油system 油being 油modelled 油 ≒ T 油is 油a 油set 油of 油rules 油which 油[...] 油describe 油the 油behaviour 油of 油a 油creative 油agent 油as 油it 油 traverses 油the 油conceptual 油space 油from 油known 油artefacts 油to 油unknown 油ones 油[...] 油and 油 possibly 油back 油again 油 ≒ R 油is 油a 油set 油of 油rules, 油expressed 油using 油the 油language 油L, 油which 油select 油an 油acceptable 油or 油 relevant 油subset 油of 油U 油which 油corresponds 油with 油Bodens1 油conceptual 油space 油 油 ≒ is 油a 油set 油of 油rules 油by 油which 油value 油is 油attributed 油to 油a 油created 油artefact 油 油 4 油ICCBR-足15 油 28 油September 油2015 油
  • 6. Creative Systems 5 油ICCBR-足15 油 28 油September 油2015 油 (Ritchie 油2007): 油 ≒ set 油of 油basic 油items 油B 油= 油data 油types 油(e.g. 油string 油of 油words, 油arrays 油of 油pixels) 油 characterising 油the 油artefacts 油produced 油by 油the 油program 油 ≒ set 油of 油results 油R 油= 油set 油of 油artefacts 油produced 油by 油the 油program 油with 油a 油 speci鍖c 油set 油of 油setting 油parameters 油 ≒ inspiring 油set 油I: 油The 油construction 油of 油the 油program 油is 油in鍖uenced 油(either 油 explicitly 油or 油implicitly) 油by 油some 油subset 油of 油the 油available 油basic 油items. 油This 油 subset, 油which 油we 油will 油call 油the 油inspiring 油set, 油could 油be 油all 油the 油relevant 油 artefacts 油known 油to 油the 油program 油designer, 油or 油items 油which 油the 油 program 油is 油designed 油to 油replicate, 油or 油a 油knowledge 油base 油of 油known 油 examples 油which 油drives 油the 油computation 油within 油the 油program. 油 油
  • 7. Creative Systems 6 油ICCBR-足15 油 28 油September 油2015 油 (Ritchie 油2007): 油 ≒ typ(X) 油= 油value 油of 油typicality 油associated 油to 油the 油 artefact 油X 油 ≒ val(X) 油= 油value 油of 油quality 油associated 油to 油X 油 ≒ T留,硫(X) 油= 油{x 油 油X 油| 油留 油 油typ(X) 油 油硫} 油 ≒ V留,硫(X) 油= 油{x 油 油X 油| 油留 油 油val(X) 油 油硫} 油
  • 8. B Set 油of 油basic 油items 油
  • 10. B I 油 Set 油of 油results 油 R
  • 11. B I 油 R Typical 油artefacts 油 T留,1(R) 油= 油{x 油 油R 油| 油留 油 油typ(X) 油 油1} 油 T留,1(R) 油
  • 12. B I 油 R Valuable 油artefacts 油 V粒,1(R) 油= 油{x 油 油R 油| 油粒 油 油val(X) 油 油1} 油 V粒,1(R) 油
  • 13. The Fractal Tree 12 油ICCBR-足15 油 28 油September 油2015 油
  • 14. 28 油September 油2015 油ICCBR-足15 油 13 油
  • 15. The 油Fractal 油Tree 油 28 油September 油2015 油ICCBR-足15 油 14 油
  • 16. 28 油September 油2015 油ICCBR-足15 油 15 油
  • 17. 28 油September 油2015 油ICCBR-足15 油 16 油
  • 18. 28 油September 油2015 油ICCBR-足15 油 17 油
  • 19. 28 油September 油2015 油ICCBR-足15 油 18 油
  • 20. 28 油September 油2015 油ICCBR-足15 油 19 油
  • 21. 28 油September 油2015 油ICCBR-足15 油 20 油
  • 22. 28 油September 油2015 油ICCBR-足15 油 21 油
  • 23. 28 油September 油2015 油ICCBR-足15 油 22 油
  • 24. 28 油September 油2015 油ICCBR-足15 油 23 油
  • 25. 28 油September 油2015 油ICCBR-足15 油 24 油
  • 26. 28 油September 油2015 油ICCBR-足15 油 25 油
  • 27. 28 油September 油2015 油ICCBR-足15 油 26 油
  • 28. 28 油September 油2015 油ICCBR-足15 油 27 油
  • 29. 28 油September 油2015 油ICCBR-足15 油 28 油
  • 30. 28 油September 油2015 油ICCBR-足15 油 29 油
  • 31. 28 油September 油2015 油ICCBR-足15 油 30 油
  • 32. 28 油September 油2015 油ICCBR-足15 油 31 油
  • 33. 28 油September 油2015 油ICCBR-足15 油 32 油
  • 34. 28 油September 油2015 油ICCBR-足15 油 33 油
  • 35. 28 油September 油2015 油ICCBR-足15 油 34 油
  • 36. 28 油September 油2015 油ICCBR-足15 油 35 油
  • 37. Observations 油 ≒ Shape 油types: 油polygon, 油snow 油鍖ake, 油vegetable 油 ≒ Shape 油dimensions: 油curvature, 油aperture, 油 symmetry 油 ≒ Optimal 油con鍖gurations 油 28 油September 油2015 油ICCBR-足15 油 36 油
  • 38. Main Analogies Creative 油System 油 37 油ICCBR-足15 油 28 油September 油2015 油 Problem 油Solver 油 Dynamical 油System 油
  • 39. Creative System as Dynamical System What 油is 油a 油path 油in 油the 油square 油of 油fractal 油trees? 油 1. A 油search 油in 油the 油conceptual 油space 油of 油a 油creative 油system 油 2. A 油trajectory 油in 油the 油phase 油space 油of 油a 油dynamical 油system 油 An 油attractor 油is 油a 油set 油of 油states 油(i.e., 油elements 油of 油the 油state 油 space 油of 油a 油dynamical 油system) 油towards 油which 油a 油set 油of 油 dynamical 油paths 油tend 油to 油evolve. 油 The 油set 油of 油dynamical 油paths 油pointing 油to 油the 油attractor 油is 油 called 油basin 油of 油attraction. 油 38 油ICCBR-足15 油 28 油September 油2015 油
  • 40. Basin Jumping and Creativity ≒ The 油conceptual 油space 油can 油be 油decomposed 油in 油basins 油of 油attraction. 油 油 ≒ Starting 油from 油a 油set 油of 油past 油examples 油(inspiration 油set), 油a 油creative 油system 油 can 油reach 油 油from 油which 油a 油speci鍖c 油basin 油of 油attraction 油can 油be 油explored. 油 ≒ Classic 油CBR 油allows 油a 油creative 油system 油to 油explore 油the 油basin 油of 油 attraction 油containing 油the 油set 油of 油past 油examples 油(assumed 油to 油be 油the 油 inspiration 油set) 油 ≒ Creative 油CBR 油should 油allows 油a 油creative 油system 油to 油reach 油basin 油of 油 attractions 油not 油containing 油the 油past 油examples 油 ≒ In 油summary, 油if 油we 油assume 油the 油creativity 油as 油a 油search 油in 油the 油conceptual 油 space, 油a 油higher 油degree 油of 油creativity 油is 油associated 油to 油the 油search 油of 油new 油 basins 油of 油attraction 油(basin 油jumping). 油 油 39 油ICCBR-足15 油 28 油September 油2015 油
  • 41. Double Similarity ≒ CBR 油is 油based 油on 油the 油capability 油to 油recognize 油a 油new 油case 油as 油 similar 油to 油one 油of 油the 油past 油cases 油 ≒ Creative 油CBR 油should 油employ 油two 油forms 油of 油similarity: 油 ≒ T-足Similarity: 油degree 油to 油which 油two 油artefacts 油are 油recognised 油as 油 belonging 油to 油the 油same 油type 油 ≒ V-足Similarity: 油degree 油to 油which 油the 油value 油of 油two 油artefacts 油is 油 recognised 油as 油similar 油 ≒ T-足similarity 油allows 油the 油system 油to 油explore 油the 油current 油basin 油 of 油attraction 油 ≒ V-足similarity 油allows 油the 油system 油to 油reach 油di鍖erent 油basins 油of 油 attraction 油 40 油ICCBR-足15 油 28 油September 油2015 油
  • 42. Types of Attraction Basins ≒ Types 油of 油artefacts 油 ≒ Creative 油Ideation: 油di鍖erent 油renderings 油of 油the 油 same 油idea 油 ≒ Components 油of 油an 油artefact 油(e.g. 油lexical 油 component 油of 油a 油text) 油 ≒ Di鍖erent 油styles 油or 油patterns 油 41 油ICCBR-足15 油 28 油September 油2015 油
  • 43. Summary of Key Ideas ≒ Analogies 油 ≒ problem 油solving: 油state/search 油space 油 ≒ generative 油system: 油space 油of 油con鍖guration 油 ≒ creative 油system: 油conceptual 油space 油 ≒ dynamical 油system: 油phase 油space 油 ≒ CBR: 油past 油examples, 油inspiring 油set 油and 油basin 油of 油 attraction 油 ≒ Multiplicity 油of 油attraction 油basins 油 ≒ Double 油similarity 油and 油basin 油jumping 油 42 油ICCBR-足15 油 28 油September 油2015 油
  • 44. Future Work ≒ Exploiting 油creative 油systems 油complexity 油(Typ 油vs. 油 Val, 油truth 油inference 油vs. 油valence 油inference) 油 ≒ Application 油to 油鍖ctional 油ideation: 油di鍖erent 油 renderings 油of 油the 油same 油idea 油 ≒ Application 油to 油linguistic 油creativity: 油 parametrisation 油and 油connection 油of 油di鍖erent 油 patterns 油 43 油ICCBR-足15 油 28 油September 油2015 油
  • 45. References ≒ G. 油Wiggins 油(2006). 油Searching 油for 油Computational 油 Creativity. 油New 油Generation 油Computing, 油24(3). 油 ≒ G. 油Ritchie 油(2007). 油Some 油Empirical 油Criteria 油for 油 Attributing 油Creativity 油to 油a 油Computer 油Program. 油 Minds 油and 油Machines, 油17(1). 油 ≒ R. 油Gibbs 油(2012). 油Metaphors, 油snow鍖akes, 油and 油 termite 油nests. 油How 油nature 油creates 油such 油beautiful 油 things. 油Chapter 油published 油in: 油Metaphor 油in 油Use: 油 Context, 油culture, 油and 油communication. 油 油Amsterdam: 油 John 油Benjamins. 油 44 油ICCBR-足15 油 28 油September 油2015 油