1. ⁘  ⁘  ⁘
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  33. Brand, Stewart 4
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  35. Brooks, Frederick P. 22
  36. Broskoski, Charles 6
  37. brutalism 7
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  39. bureaucracy 12
  40. Burnham, Bo 9
  41. business 15
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  43. Cagan, Marty 8
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  50. chance 11
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  53. childhood 6
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  55. choice 8
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  58. Cleary, Thomas 8
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  63. color 23
  64. commonplace 11
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  66. community 7
  67. complexity 11
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  72. Corbusier, Le 13
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  76. crime 9
  77. Critchlow, Tom 5
  78. critique 10
  79. Cross, Nigel 12
  80. Cross, Anita Clayburn 10
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  90. Debord, Guy 6
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  93. details 31
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  95. Dieste, Eladio 4
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  102. Eatock, Daniel 4
  103. economics 13
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  106. Eliot, T.S. 14
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  177. Isaacson, Walter 28
  178. Ishikawa, Sara 33
  179. iteration 13
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  191. Keqin, Yuanwu 8
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  217. making 77
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  222. material 39
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  225. meaning 33
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  227. melancholy 52
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  230. metrics 19
  231. microsites 49
  232. Miller, J. Abbott 10
  233. Mills, C. Wright 9
  234. minimalism 10
  235. Miyazaki, Hayao 30
  236. Mod, Craig 15
  237. modularity 6
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math

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  • To worship at the shrine of mathematics

    The new [physics-based] viewpoint is so potent that it has perhaps, caused too many metallurgists to forsake their partially intuitive knowledge of the nature of materials to worship at the shrine of mathematics, a trend reinforced by the curious human tendency to laud the more abstract.

    Matter versus Materials: A Historical View
    • math
    • abstraction
  • On beauty bare

    Even more than Euclid, hath Euler gazed on beauty bare.

    Structure, Substructure, and Superstructure
    • math
    • beauty

    Referring to the Euler characteristic.

  • Wang tiles

    Image from en.wikipedia.org on 2020-09-01 at 4.15.58 PM.png

    Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.

    The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern.

    In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem.

    Wikipedia
    en.wikipedia.org
    1. ​​Truchet Tiles​​
    2. ​​The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy​​
    • math
    • algorithms
  • Trees and graphs

    a-tree-is-a-kind-of-graph;scale=400,400

    A tree is a kind of graph, but a graph can be considerably more complex than a tree.

    I have reason to believe, which for brevity’s sake I will treat elsewhere, that the most complex class of processes and structures we humans can consciously prescribe, reduces mathematically to a tree. A tree has a top, bottom, left and right. Its branches fan out from the trunk and they don’t intersect with one another. They are discrete, contiguous, identifiable objects which persist across time. Trees are Things.

    Software and websites, however, reduce to arbitrarily more complex structures: they are graphs. A graph has no meaningful orientation whatsoever. No sequence, no obvious start or end—at least none that we can intuit. It is better considered not as one Thing, but as a federation of Things, like the brain or a fungus network, or perhaps a composite artifact left behind from an ongoing process, like an ant colony or human city.

    Dorian Taylor, On the "Building" of Software and Websites
    1. ​​A City Is Not a Tree​​
    • networks
    • thinking
    • math
  • Trees and semilattices

    Semilattice.jpg

    The tree of my title is not a green tree with leaves. It is the name of an abstract structure. I shall contrast it with another, more complex abstract structure called a semilattice.

    Both the tree and semilattice are ways of thinking about how a large collection of many small systems goes to make up a large and complex system.

    A collection of sets forms a semilattice if, and only if, when two overlapping sets belong to the collection, the set of elements common to both also belongs to the collection. That is, if [234] and [345] belong to the collection, then [34] belongs to the collection.

    A collection of sets forms a tree if, and only if, for any two sets that belong to the collection either one is wholly contained in the other, or they are wholly disjoint. Every tree is trivially a simple semilattice.

    We are concerned with the difference between structures in which no overlap occurs, and those structures in which overlap does occur.

    The semilattice is potentially a much more complex and subtle structure than a tree. It is this lack of structural complexity, characteristic of trees, which is crippling our conceptions of the city.

    Christopher Alexander, A City Is Not a Tree
    • math
  • A City Is Not a Tree

    An Essay by Christopher Alexander
    www.patternlanguage.com
    1. ​​Strands of life​​
    2. ​​Impending destruction​​
    3. ​​The right overlap​​
    4. ​​The difficulty of designing complexity​​
    5. ​​Political chains of influence​​
    1. ​​Trees and graphs​​
    2. ​​The dishonest mask of pretended order​​
    3. ​​The problem with trees​​
    4. ​​Both practical and aesthetic concerns​​
    • cities
    • urbanism
    • design
    • architecture
    • math
  • Notes on the Synthesis of Form

    A Book by Christopher Alexander
    www.hup.harvard.edu
    1. ​​I could do better than that​​
    2. ​​This small internal quaver​​
    3. ​​Their wrongness is somehow more immediate​​
    • math
    • design
    • architecture
    • form
    • problems
  • Visualizing Data

    A Book by William S. Cleveland
    • visualization
    • math
  • Exploratory Data Analysis

    A Book by John Tukey
    • math
    • visualization
  • Plus Equals #4

    An Article by Rob Weychert
    plusequals.art
    D7857F89-2270-4B41-880F-3534F6B8DE77.jpeg

    One of the seeds for Plus Equals was planted a few years ago with Incomplete Open Cubes Revisited, my extension of a Sol LeWitt work. I learned a lot about isometric projection from that project, but my affection for the concept didn’t begin there. Whether I’m looking at a Chris Ware illustration or an exploded-view technical drawing of a complex machine, an isometric rendering always stirs something in me.

    1. ​​Isometry​​
    2. ​​Little Blank Riding Hood​​
    • geometry
    • math
    • visualization
  • A brief foray into vectorial semantics

    An Article by James Somers
    jsomers.net

    One of the best (and easiest) ways to start making sense of a document is to highlight its “important” words, or the words that appear within that document more often than chance would predict. That’s the idea behind Amazon.com’s “Statistically Improbable Phrases”:

    Amazon.com’s Statistically Improbable Phrases, or “SIPs”, are the most distinctive phrases in the text of books in the Search Inside!™ program. To identify SIPs, our computers scan the text of all books in the Search Inside! program. If they find a phrase that occurs a large number of times in a particular book relative to all Search Inside! books, that phrase is a SIP in that book.

    • math
    • meaning
    • words
    • notetaking
    • search
    • chance
  • tixy.land

    A Website
    tixy.land
    Screenshot of tixy.land on 2020-11-11 at 2.42.41 PM.png

    sin(t * x) * cos(t * y)

    Creative code golfing.

    • code
    • math
    • visualization
    • microsites
  • Rafael Araujo's Golden Ratio

    A Gallery
    www.rafael-araujo.com
    Image from www.rafael-araujo.com on 2021-05-21 at 10.24.01 AM.webp

    Blue Morpho Double Helix & Icosahedron

    • math
    • geometry
    • art
  • The Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy

    A Research Paper by Cyril Stanley Smith
    www.jstor.org
    Screenshot of www.jstor.org on 2020-08-27 at 11.53.03 AM.png

    A pattern of tiles illustrated by Douat in 1722.

    A translation is given of Truchet's 1704 paper showing that an infinity of patterns can be generated by the assembly of a single half—colored tile in various orientations.

    1. ​​Separation and connection in all things​​
    2. ​​Corpuscles of nothing and atoms of something​​
    3. ​​The scale of resolution determines what is seen​​
    4. ​​This is history​​
    1. ​​Truchet Tiles​​
    2. ​​The Sense of Order​​
    3. ​​The Shape of Time​​
    4. ​​Wang tiles​​
    • graphics
    • math
  • Everything and More

    A Book by David Foster Wallace
    • math
  • InfoCrystal

    A Research Paper
    www.semanticscholar.org
    Screenshot of www.semanticscholar.org on 2020-08-16 at 2.32.07 PM.png

    This paper introduces a novel representation, called the InfoCrystal, that can be used as a visualization tool as well as a visual query language to help users search for information. The InfoCrystal visualizes all the possible relationships among N concepts.

    • math
    • networks
    • connection
    • visualization
    • logic

See also:
  1. visualization
  2. design
  3. architecture
  4. networks
  5. geometry
  6. cities
  7. urbanism
  8. form
  9. problems
  10. meaning
  11. words
  12. notetaking
  13. search
  14. chance
  15. connection
  16. logic
  17. thinking
  18. graphics
  19. algorithms
  20. code
  21. microsites
  22. art
  23. beauty
  24. abstraction
  1. Christopher Alexander
  2. John Tukey
  3. William S. Cleveland
  4. James Somers
  5. David Foster Wallace
  6. Dorian Taylor
  7. Cyril Stanley Smith
  8. Rob Weychert