Götz Kluge's photos

Fast Fourier Transform The blue boxes do the elementary DFT (Discrete Fourier Transform). They also are called " decimation butterflies " and perform four operations: one complex multiplication, one sign inversion and two complex additions. Usually the transformer is presented differently. This depiction of course does not change the design, but it shows the construction of the transformer using a fractal approach. In the usual presentations (of Radix-2 FFT algorithms), the butterflies cross the lines; in this presentation, lines cross lines. The numbering of inputs and outputs is binary. Why "fractal"? A 2-port DFT requires one butterfly, a 4-port DFT requires two 2-port DFTs plus two butterflies, a 8-port DFT requires two 4-port DFTs plus four butterflies, a 16-port DFT requires two 8-port DFTs plus eight butterflies, and so on. Why "butterfly"? That is because of the two "triangles" in each box. Zoomorphism works even with engineers, and in this case the pair of triangles look like the wings of a butterfly to them. First version (2005):

Tokyo 2002

Denki! - Tokyo 2003

[left]: HMS Beagle Among Porpoises (183X) by Robert Taylor Pritchett. [right]: A vessel in an illustration by Henry Holiday to Lewis Carroll's The Hunting of the Snark (1876). The shape of the vessels is pretty generic, but William Snow Harris' new lightning conductors were a special feature of the HMS Beagle.

An illustration by Henry Holiday to Lewis Carroll's The Hunting of the Snark (1876). In the red frame: The missing bell? Blue inset (just fooling around a bit): HMS Beagle Among Porpoises" (1830-1839?) by Robert Taylor Pritchett . The shapes of the vessels are pretty generic, but the lightning rod was a special feature of the HMS Beagle.

The comparison shows Henry Holiday's illustration (1876) to the front cover of Lewis Carroll's The Hunting of the Snark compared to a reproduction of the Ditchley Portrait (a gift from Sir Henry Lee to Queen Elizabeth I, c. 1592) by Marcus Gheeraerts the Younger. 2013-02-05: The allusions in Henry Holiday's Snark illustration to the Ditchley Portrait are not as easy to detect as in some other Snark illustrations by Holiday, yet this comparison holds the third rank in my set of Flickr Members' Snark Favorites . Watch the sail of the ship and the queen's "sail". "While I concede Tufail 's thesis (2003) that Holiday received his instructions from Carroll and created his illustrations to reflect Carroll's cryptic messages and allusions, I contend that the interpretations given to the words we know so well by so many illustrators over a period in excess of 130 years continue to keep the Snark alive. Furthermore, it is my personal belief that Holiday managed to slip in a few interpretations of his own even though Carroll approved of the end result." (Doug Howick: The Hiihijig of the Bijtcheb, Knight Letter #28, Summer 2009) Perhaps Tufail and Howick both are right. As Henry Holiday frequently alluded to works of father&son Gheeraerts, John Tufail's Illuminated Snark (2004) gave me the idea to search for a Gheeraerts painting in which a map is shown . John reckoned, that the clouds in Holiday's front cover illustration may be part of a map. I think that this possibility cannot be excluded. John's assumption then drew my attention to the Ditchley portrait. (The Ditchley portrait again helped me to find sources for Holiday's illustration to the back cover of Carroll's book as well.)

The image shows Henry Holiday's illustration (1876) to the front cover of Lewis Carroll's The Hunting of the Snark compared to a grey shaded reproduction of the Ditchley Portrait (a gift from Sir Henry Lee to Queen Elizabeth I, c. 1592) by Marcus Gheeraerts the Younger. "While I concede Tufail 's thesis (2003) that Holiday received his instructions from Carroll and created his illustrations to reflect Carroll's cryptic messages and allusions, I contend that the interpretations given to the words we know so well by so many illustrators over a period in excess of 130 years continue to keep the Snark alive. Furthermore, it is my personal belief that Holiday managed to slip in a few interpretations of his own even though Carroll approved of the end result." (Doug Howick: The Hiihijig of the Bijtcheb, Knight Letter #28, Summer 2009) Perhaps Tufail and Howick both are right. There is more: "The 'clouds' - or what at first glance appear to be clouds, are another item of considerable interest. If these are indeed supposed to represent clouds, then they are remarkably poor renditions (and Holiday was by no means either a poor, nor slipshod artist). Rather any close examination of this aspect of the illustration leads the observer to think that this background to the Bellman is actually a map, complete with rivers. contrast to the map Bellman presents to his admiring crew." (John Tufail, The Illuminated Snark , 2004) As Henry Holiday in his Snark illustrations frequently alluded to works of father&son Gheeraerts, John Tufail's Illuminated Snark gave me the idea to search for a Gheeraerts painting in which a map is shown . John reckoned, that the clouds in Holiday's front cover illustration may be part of a map. I think that this possibility cannot be excluded. John's assumption then drew my attention to the Ditchley portrait. (The Ditchley portrait again helped me to find sources for Holiday's illustration to the back cover of Carroll's book as well.) 2013-12: Evidence supporting of John Tufail's thesis: www.doylenewyork.com/asp/fullcatalogue.asp?salelot=13BP04+++553+&refno=++953647&image=0 (see also: groups.yahoo.com/neo/groups/carrolliana/conversations/topics/358 )

[left]: Henry Holiday's back cover illustration (1876) to Lewis Carroll's The Hunting of the Snark . [right]: Allegorical English School painting (ca. 1610, redrawn and rearranged: 2013) of Queen Elizabeth I at Old Age with allegory of Death and Father Time . (Location of original painting: Corsham Court, EAN-Number: 4050356835081) www.corsham-court.co.uk/Pictures/Commentary.html : "This portrait of Elizabeth I illustrates the difficulties she encountered during her troubled reign. For example, conflict between Protestants and Catholics was rife and the re-drafting of the Book of Common Prayer (held in her left hand) was a sensitive issue of the time." Changes of lower segment: Shifted mirror view

[left]: Segment from an Illustration by Henry Holiday to Lewis Carroll's The Hunting of the Snark (1876). [right, mirror view]: The Bone Player (1856) by William Sidney Mount, now displayed in MFA, Boston. · · 513 · · He was black in the face, and they scarcely could trace · · 514· · · · The least likeness to what he had been: · · 515· · While so great was his fright that his waistcoat turned white- · · 516· · · · A wonderful thing to be seen! · · 517· · To the horror of all who were present that day. · · 518· · · · He uprose in full evening dress, · · 519· · And with senseless grimaces endeavoured to say · · 520· · · · What his tongue could no longer express. · · 521· · Down he sank in a chair--ran his hands through his hair-- · · 522· · · · And chanted in mimsiest tones · · 523· · Words whose utter inanity proved his insanity, · · 524· · · · While he rattled a couple of bones. Mahendra Singh guided me to this painting. I found a painting depicting a bone player in his blog which Mahendra used to tell us something about the bone ratteling Banker. Mahendra is a professional illustrator who not only is one of the few curageous and curious Snark hunters, but also (like Holiday) a very gifted architect of Snark conundrums in his own right. Just look at his own illustrations to his Snark edition (2010). ( justtheplaceforasnark.blogspot.com/2012/01/fit-7-pg-752-d... ) Mount painted The Bone Player after receiving a commission from the printers Goupil and Company for two pictures of African-American musicians to be lithographed (e.g. by Jean-Baptiste Adolphe Lafosse ) for the European market. These became the last in a series of five life-size likenesses of musicians that Mount executed between 1849 and 1856. ( www.mfa.org/collections/object/the-bone-player-33207 ) Could Henry Holiday have seen that lithograph? In London, Goupil & Cie was established by Ernest Gambart. 17 Southampton Street. Moved to 25 Bedford Street, Strand in 1875 when Goupil & Cie took over Holloway & Sons and their salerooms. Goupil's manager in London was at this time Charles Obach. ( en.wikipedia.org/wiki/Goupil_&_Cie )

Harajuku, Tokyo, 2002

Festival in Asakusabashi (Tokyo), June 2002

[left]: Segment from an Illustration by Henry Holiday to Lewis Carroll's The Hunting of the Snark (1876). [right, mirror view]: The Bone Player (1856) by William Sidney Mount, now displayed in MFA, Boston. · · 513 · · He was black in the face, and they scarcely could trace · · 514· · · · The least likeness to what he had been: · · 515· · While so great was his fright that his waistcoat turned white- · · 516· · · · A wonderful thing to be seen! · · 517· · To the horror of all who were present that day. · · 518· · · · He uprose in full evening dress, · · 519· · And with senseless grimaces endeavoured to say · · 520· · · · What his tongue could no longer express. · · 521· · Down he sank in a chair--ran his hands through his hair-- · · 522· · · · And chanted in mimsiest tones · · 523· · Words whose utter inanity proved his insanity, · · 524· · · · While he rattled a couple of bones. Mahendra Singh guided me to Mount's painting. I found a painting depicting a bone player in his blog which Mahendra used to tell us something about the bone ratteling Banker. Mahendra is a professional illustrator who not only is one of the few curageous and curious Snark hunters, but also (like Holiday) a very gifted architect of Snark conundrums in his own right. Just look at his own illustrations to his Snark edition (2010). ( justtheplaceforasnark.blogspot.com/2012/01/fit-7-pg-752-d... ) Mount painted The Bone Player after receiving a commission from the printers Goupil and Company for two pictures of African-American musicians to be lithographed (e.g. by Jean-Baptiste Adolphe Lafosse ) for the European market. These became the last in a series of five life-size likenesses of musicians that Mount executed between 1849 and 1856. ( www.mfa.org/collections/object/the-bone-player-33207 ) Could Henry Holiday have seen that lithograph? In London, Goupil & Cie was established by Ernest Gambart. 17 Southampton Street. Moved to 25 Bedford Street, Strand in 1875 when Goupil & Cie took over Holloway & Sons and their salerooms. Goupil's manager in London was at this time Charles Obach. ( en.wikipedia.org/wiki/Goupil_&_Cie )

see also www.ipernity.com/doc/goetzkluge/21710521 for the Haskell version

=== The Bellman's rule === 001 · · "Just the place for a Snark!" the Bellman cried, 002· · · · As he landed his crew with care; 003· · Supporting each man on the top of the tide 004· · · · By a finger entwined in his hair. 005· · "Just the place for a Snark! I have said it twice: 006· · · · That alone should encourage the crew. 007· · Just the place for a Snark! I have said it thrice: 008· · · · What I tell you three times is true." === Implementation of the rule === The little Haskell program checks whether entries in a list of statements occur three times (or more). Therefore the program is a useful tool to test the truth of statements.

"A sailing ship: the brig H. M. S. Beagle . It is commanded by the bigoted Captain Robert Fitz Roy. The year is 1831. On board, a brain explosion. With a delay of about two centuries of Physics, it is shattered by the the Galileo of Biology. The following stages: In 1838 the theory of natural selection was completed. In 1859 comes the Origin of Species. · · Fade-over. · · When it returns into the scene, it is still a ship. A sailing ship, of course. The Beagle took to the sea again? The year is 1874: Darwin is still alive, well and chatty." (Adriano Orefice) Images: [left]: Illustration "He had wholly forgotten his name" by Henry Holiday to Lewis Carroll's The Hunting of the Snark (1876) [right]: "Crossing the Line" (1839), redrawn (2013) based on a print by Thomas Landseer, after Augustus Earle. The print you will find in Robert Fitz-Roy's Narrative of the surveying voyages of HMS Adventure and Beagle , Vol II (1839). This comparison is related to my assumption that Lewis Carroll's and Henry Holiday's The Hunting of the Snark at least partially has been inspired by Charles Darwin's explorational Beagle voyage.

Detail from Henry Holiday's illustration to the back cover of Lewis Carroll's The Hunting of the Snark (1876). I don't unterstand this pattern (if it is a pattern). Perhaps it is not meant to be understood. Or it is no "meaningful" pattern at all. The pattern is clearly distinguishable from its environment. The letter-like shapes shown below the image are the result of very simple linear transformations using GIMP. Yet, I still can't say whether these are letters or just meaningless shapes. Is there any meaning? Should the "letters" be rotated and/or mirrored again? Is there a word game ("Anne I" beside a buoy) related to Anne Boleyn? (In his illustrations, Holiday clearly alluded to other historical figures related to Anne Bolyen, e.g. Queen Elizabeth I.)

Segment of an illustration by Henry Holiday (cut by Joseph Swain) in Lewis Carroll's The Hunting of the Snark , 1876 The segment on the lower right side is Charles Darwin's Tree of Evolution or Tree of Life sketch in his 1st notebook, page 36, 1837-1838. I learned, that Darwin did not keep his notebook secret after the publication of On the Origin of Species , but I do not know of any presentation of his sketch before 1876. Thus, the resemblance between the "weed" and Darwin's evolutionary tree sketch propably is purely incidental. Postprocessing: GIMP perspective transformation tool Questions: (1) When did Charles Darwin publish a facsimile of his sketch fo the first time? When (e.g. in lectures etc.) was it presented for the first time? (2) Or is there a completely different explanation? Holiday's "weed" also could allude to an eagle riding a wild boar .

Henry Holiday's depiction of the Bellman in fhe front cover illustration to Lewis Carroll's The Hunting of the Snark and Father Time from an allegorical English School painting (ca. 1610) depicting Queen Elizabeth I at Old Age . That which hath made them drunk hath made me bold; What hath quench'd them hath given me fire. Hark! Peace! It was the owl that shriek'd, the fatal bellman, Which gives the stern'st good-night. He is about it: The doors are open; and the surfeited grooms Do mock their charge with snores: I have drugg'd their possets, That death and nature do contend about them, Whether they live or die.