Tangles and Paradox

Index of topics:
  1. Selected Paradoxical Drawings
  2. Forming Tangles and Tangle Notations
  3. Knot tiles and knot tilings
  4. Converting Tangles to Paradoxes
  5. Primitives and Tapestries of Paradox
  6. Related topics
  7. Additional references

Selected Paradoxical Drawings (various authors)

Magritte horse in forest

ElloParadoxArt

paradox textile

Explanation

Explanation    Link
MWM Graphics

Link/Explanation

Bird with implied line segments

cat deity

Paradoxical Drawing

Link

Cat Deity: Link  and Explanation

Link Explanation Link

 

SVGParadox

Pipeworks -- multidimensional flow chart c. 1972, 2016
Foot - Dailey, 1972 - 2016
Link Welcome to the Pipeworks
Foot
 
Abstractionfire of hephaestusFlower - escherian view
Abstraction: Link ExplanationFire of Hephaestus (1975-2016)  Link ExplanationFlower (1973? - 2016) Link Explanation

Forming Tangles and Tangle Notations
Animated illustration of the drawing of regular graphs in the plane Drawing Regular Graphs
http://cs.sru.edu/~ddailey/tangles/TangleDrawing.svg
Animation and explanation of the drawing of a tangle
Animated drawing of tangles.
Drawing four-regular Graphs (tangles)
http://cs.sru.edu/~ddailey/tangles/TangleDrawing1.svg
Animated Drawing of Tangles https://ello.co/ddailey/post/hzokhzodcsorwfkjfjdoyw
and
http://cs.sru.edu/~ddailey/tangles/TangleDrawing3.svg
and (story with links)
https://ello.co/ddailey/post/xwsushuzb93pbwfwgpaqfg
and
http://cs.sru.edu/~ddailey/tangles/TangleDrawing.svg
drawing tangles  BasicTangles
http://cs.sru.edu/~ddailey/tangles/BasicTangles.svg

https://ello.co/ddailey/post/A8uFJlY0MGAPom08-kw70g
 
 
Tangles with one node https://ello.co/ddailey/post/OTgTi1Dqfpl9W_8GKcVaew
http://cs.sru.edu/~ddailey/paradox/TanglesE1.svg
The four tangles on two nodes https://ello.co/ddailey/post/Qhzy2lCKbkzbSl6mIpsemw
http://cs.sru.edu/~ddailey/paradox/TanglesE2.svg
Loopless tangles on three and four nodes https://ello.co/ddailey/post/UMhp8MqALvu7YBfiEp9MkA
http://cs.sru.edu/~ddailey/paradox/TanglesE3.svg
Some relations between tangles and graphs https://ello.co/ddailey/post/cbqDsprl15zyMloJ52DkCg
http://cs.sru.edu/~ddailey/paradox/TanglesE4.svg
Two tangles; one graph https://ello.co/ddailey/post/LWj6o9OnguAOneFq5ztFbw
http://cs.sru.edu/~ddailey/tangles/transform8to8A.svg
and
https://ello.co/ddailey/post/uvruyxd_wiezxgtlhcuyrq
and
http://cs.sru.edu/~ddailey/tangles/tangleAnimStrokeAndPath.svg

Optimizing tangles https://ello.co/ddailey/post/s1dgzharyirqarfz0fuiig
and
http://cs.sru.edu/%7Eddailey/canterbury/knot2.svg
and
http://cs.sru.edu/~ddailey/svg/tanglecar.svg
and
http://cs.sru.edu/~ddailey/svg/squig1.svg
Tangles with Periodic Notation https://ello.co/ddailey/post/FB6wF3nOvyafszVsHxsL_A Another periodic series of Tangles
http://cs.sru.edu/~ddailey/tangles/OS12345.svg
also
https://ello.co/ddailey/post/ha6lae86bzibimtrvmivuw
and
http://cs.sru.edu/~ddailey/tangles/oneTangledNotation.svg
Roots (Radicals) of Tangles https://ello.co/ddailey/post/Jflp3QBXbFb8MXuYy3f7QQ  Roots of Tangles
http://cs.sru.edu/~ddailey/tangles/tangles1.svg
[https://ello.co/ddailey?start_timestamp=2015-12-12]
first notation for tangles https://ello.co/ddailey/post/jcqhtoop0jmrjhpclmyaug
and
http://cs.sru.edu/~ddailey/tangles/TangleDrawing5.svg
Basic Loops https://ello.co/ddailey/post/MMVmNWXfqfIH9rQHQ4voJg Basic Loops
http://cs.sru.edu/~ddailey/tangles/basicLoops.svg
Venn diagrams on five sets Applied Tangles
http://cs.sru.edu/~ddailey/canterbury/knot2.svg
Venn diagrams on five sets
Notation Development Picture https://ello.co/ddailey/post/crg4c5fh-sdd0kclua3wqq
and
http://cs.sru.edu/~ddailey/tangles/TangleDrawing4.svg
Challenges for flow and drawing https://ello.co/ddailey/post/vc4qvxtk5co8ggckcgkzug
and
http://cs.sru.edu/~ddailey/tangles/basicLoops4.svg

Knot tiles,  knot tilings, and weaves
Systematic Knot Alphabet http://cs.sru.edu/~ddailey/tiling/SystematicKnotsS.svg Systematic Knots
Also here and here and prototyle and Pulse{blood,bile, phlegm}
[https://ello.co/ddailey?start_timestamp=2015-08-10]
Knot Travel Animated GIF https://ello.co/ddailey/post/s9_iCFosVb26uYS3-kUfqA changing knots
Actual animated GIF file
http://cs.sru.edu/~ddailey/tiling/AskKnot.svg
http://cs.sru.edu/~ddailey/tiling/KnotsFollow.svg (3 cars)
[https://ello.co/ddailey?start_timestamp=2015-08-27]
triangular knot tiles https://ello.co/ddailey/post/Y7qBkhbkwSr1nnU_ffEySA
http://srufaculty.sru.edu/david.dailey/svg/tribraids9.svg
from SVGOpen 2008
overlapping circles making foam of euler diagrams https://ello.co/ddailey/post/K7L2Ud0nKxmYV50An7T3QQ
http://cs.sru.edu/~ddailey/tiling/EulerFoam3.svg
wallpaper from messages with tangle alphabets http://srufaculty.sru.edu/david.dailey/javascript/traverse.html
Wallpaper from messages with tangle alphabets (circa 1999)
SVG weave using gradients http://srufaculty.sru.edu/david.dailey/svg/gradientweave.svg
Screen shot of picture weaver Weaving pictures with arbitrary weaves
http://cs.sru.edu/~ddailey/weave/weaver0.htm
http://granite.sru.edu/~ddailey/weave/weaver1.htm

Knot and tangle traversal 
Trefoil knot traffic http://cs.sru.edu/~ddailey/canterbury/knot2.svg
Borromean rings with traffic http://cs.sru.edu/~ddailey/canterbury/rings.svg
animated traffic and signals https://ello.co/ddailey/post/svrwnvcaimzgzin7e5hx3q
and
http://cs.sru.edu/~ddailey/tangles/drawingcurve7.svg
Animated Dali clock https://ello.co/ddailey/post/reprz6aca54l1fkxzxwcrg
and
http://cs.sru.edu/~ddailey/tangles/drawingcurve.svg
Worms dancing on a tangle https://ello.co/ddailey/post/_f5pnm2pnnealscgtdi-nq
http://cs.sru.edu/~ddailey/tangles/AnimTangleStroke.svg
and
https://ello.co/ddailey/post/njehg970lvz3tqzkevd-tg
http://cs.sru.edu/~ddailey/tangles/SimpleStrokingOfTangle1.svg (tortoise and hare)

Converting Tangles to Paradoxes
Making Paradoxes from Tangles https://ello.co/ddailey/post/z_zXmFuYBmruwJtU5ODp3Q
http://cs.sru.edu/~ddailey/paradox/TanglesE5.svg
Steps in converting tangles to paradoxes https://ello.co/ddailey/post/ytUERkybISdfVMMqsVmlWg
http://cs.sru.edu/~ddailey/tangles/knotscolor2.svg

VennParadoxes


 

Link

TangleParadoxes


 

Link

Borromean Paradox


 

Link


tangles to paradox https://ello.co/ddailey/post/Z5v7fTKbj4aslKOVXsOQnQ
http://cs.sru.edu/~ddailey/paradox/tangles6.svg
and
https://ello.co/ddailey/post/glgy-9c3rr7w0d8bfazo0q
and
http://cs.sru.edu/~ddailey/tangles/tangledox.svg

simple paradoxes


Link

Explanation

Ello Links to Paradox Posts https://ello.co/ddailey/post/AruOaL7VD3UyaONZ6Tvyhw tangle AND paradox (many links)
http://cs.sru.edu/~ddailey/ello/paradox/tangleANDparadox.html
earth wobble https://ello.co/ddailey/post/b8oxehs38hyfjadsyvfbla
and
http://cs.sru.edu/%7Eddailey/tangles/pentatanglesS.svg

Primitives and Tapestries of Paradox
making an alphabet of paradox https://ello.co/ddailey/post/QW4a4J6p5Uvt-ksqM4NNqw Alphabet of Paradox
http://cs.sru.edu/~ddailey/paradox/paradox8a.svg
[https://ello.co/ddailey?start_timestamp=2015-11-12]
alphabet Paradox https://ello.co/ddailey/post/0ZXhYx8xtnQi0KdJYqdDmg  Alphabets for Paradox
http://cs.sru.edu/~ddailey/paradox/paradoxesCount2.svg
tapestry of Paradox https://ello.co/ddailey/post/F7icJH9iXbyGZ1PjDtX1Xw  Tapestry of Paradox
http://cs.sru.edu/~ddailey/paradox/PTapestry3.svg
[https://ello.co/ddailey?start_timestamp=2015-11-01]
Making Squares for a Paradox Quilt https://ello.co/ddailey/post/QoNqyS9XQyqhSnX-plJ1-g Paradoxes from Tangles (with links)
http://cs.sru.edu/~ddailey/paradox/Paradox2a.svg
paradoxTapestryClear https://ello.co/ddailey/post/q8EqiNyzYhQUbKLFHA9g2g Paradox Tiles
http://cs.sru.edu/~ddailey/paradox/family8Clear.svg
paradox tapestry https://ello.co/ddailey/post/LUIC1c7uCLxhpn5Quw2Jjw Paradox Tiles (colored)
http://cs.sru.edu/~ddailey/paradox/family8Color.svg
[https://ello.co/ddailey?start_timestamp=2015-11-13]
Solar Flares with paradoxical alphabet tessellation Solar Flares: Tessellation by Alphabet of Paradox
https://ello.co/ddailey/post/trCpEf6p_Lye8rqDDqsGtg
http://cs.sru.edu/~ddailey/paradox/eggP2.svg
Tiling with a single glyph Super-strong carbon mesh with quinary memory. (Simple nondeterministic paradoxical tessellation)
http://cs.sru.edu/~ddailey/paradox/fourtile.svg
skewed paradoxical tiling with strata The Pennsylvanian period (mit Frack´┐Żng und Paradox)
http://cs.sru.edu/~ddailey/paradox/OddParadox.svg
PETScan https://ello.co/ddailey/post/dntpbya3wfz7gnnfw_c6fa
and
http://cs.sru.edu/%7Eddailey/svg/snowandflake4.svg
Screen Shot of the use of Picture Weaver http://cs.sru.edu/~ddailey/weave/weaver0.htm
https://ello.co/ddailey/post/h_JEqAozlNfpIDWTAsod4A
and
http://cs.sru.edu/~ddailey/weave/weaver1.htm
https://ello.co/booksnips/post/_I1h3lKXMvjkvg0f58f64g

Related topics
snow bubbles from paradox alphabet Snow Bubbles: tiling with ferny-tiles
https://ello.co/ddailey/post/FuLBVR20QTz4ZXsTbfmPQA
https://d324imu86q1bqn.cloudfront.net/uploads/asset/attachment/3294062/ello-xhdpi-829d2d88.jpg
glyphs made of arcs Gardens of Glyphs
https://ello.co/ddailey/post/OY0ywyhkZ2SjuAMl9e1CCA
http://cs.sru.edu/~ddailey/tiling/QuartercircleBezs.svg
and
https://ello.co/ddailey/post/zwwfBUmyvrhSVlIAEgHyqg
http://cs.sru.edu/~ddailey/tiling/CuFoam.svg
[https://ello.co/ddailey?start_timestamp=2015-08-02]
Knots and Diagrams Links http://cs.sru.edu/~ddailey/Combo/knots.html Knots and diagrams

moving seed pod


Link

Dali 33434 tessellation Another portal from tiling to paradox
Dali picture


Additional references:
http://cs.sru.edu/~ddailey/Combo/tiling.html Link to work on tessellation
http://srufaculty.sru.edu/david.dailey/weaving.htm Older experiments with weaving, knitting, knotting
http://cs.sru.edu/~ddailey/Combo/paradox.html Old Paradox index
http://cs.sru.edu/~ddailey/Combo/ComboTalk.html From Web Standards to Web Combinatorics