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# AMT/C 24-27

Work on morphogenesis. Folders of notes, calculations and diagrams, received from N.E. Hoskin in 1978, and additional to the material on the subject listed as C/7-10. The papers are part of the extensive notes and drafts left at AMT's death which some of his colleagues (R.O. Gandy, N.E. Hoskin, and B. Richards) intended to prepare for publication. The material is mainly AMT's AMS and TS, with many additions and corrections. It includes diagrams, tables, calculations, and computer routines. Sometimes both sides of the paper are used; many pages have other work on the back. Some of the material constitutes relatively substantial paginated sequences, whilst some consists of random pages which have not been assigned a definite place or description. All titles and descriptions in inverted commas are those which appear on the AMS. Later notes or comments in the hands of Hoskin and Gandy are identified and indicated wherever possible. See also Dr. J. Swinton's web pages http://www.swintons.net/jonathan/turing.htm for a detailed analysis of page sequences and contents.

Paper, 4 envelopes.

**Copyright:** Copyright © P.N. Furbank

- AMT/C/24
Folder inscribed, 'Morphogens. Turing I'. With MS note by Gandy, ' This contains consecutive pieces which were not incorporated by Hoskin and Richards in their paper'. Includes, among other unidentified pages:-

- 'Outline of the development of the daisy'. Includes sections on 'Considerations governing the choice of parameter' and 'Early stages in pattern formation'. Numbered by R.O. Gandy
- worked example of the theory in Morphogen theory of phyllotaxis II, showing how orthogonal eigenfunctions can be chosen for a linear model of diffusion between four discrete cells arranged as three satellites around a central cell
- '13 Stationary waves in continuous tissue and abstract space'
- 'Forced waves'
- 'discarded FIRSTART values'
- '4. The equations applied to a plane'
- 'Effect of quadratic terms'
- Substantial set of drafts and calculations, with [? Hoskin's] separate page heading, 'Stability and approximations'
- 'Hex stability with different values of ?'
- 'Damping due to the J term'
- draft of 'solvable and unsolvable problems' (Penguin Science News 31, 1954)
- 'Lattice solutions and their stability'
- 'Fig X': a nomogram.

- AMT/C/25
Folder inscribed, 'Morphogen. Theory of Phyllotaxis. Turing 2'. With MS note by Gandy, 'This is the draft from which Hoskin and Richards prepared their paper Part 1 (which follows the draft rather closely. Passages in light blue are I think by Hoskin)'. The Hoskin and Richards draft is catalogued at AMT/C/8. Includes:-

- AMT's TS draft, with many AMS revisions, and numbered in another hand. AMT's AMS revisions are usually in black ink, but occasionally in pencil. Other corrections and markings appear in another hand, in blue ink and pencil, and there is also some linking material on separately numbered pages, e.g. 26a, 57a
- 'Naturally occurring phyllotactic patterns'
- 'Some properties of Fibonacci numbers'
- un-numbered MS headed, 'Stability of 2
^{nd}order equations' - diagrams of florets in sunflower head, numbered and annotated by AMT
- photograph of sunflower head
- review by H.S.M. Coxeter of a book by L. Fejes Tóth, Lagerungen in der Ebene, auf der Kugel und im Raum (Berlin, 1953), reprinted from Bulletin of the American Mathematical Society (Vol. 60, Mar. 1954).

- AMT/C/26
Folder inscribed, 'Chemical Theory of Morphogenesis. Turing 3'. With MS note by R.O. Gandy, 'Part II of draft used by Hoskin and Richards'. Includes:-

- TS draft, numbered in another hand. The draft is AMT's TS, with many AMS revisions in black ink. The title on p.1, 'Part II Chemical Theory of Morphogenesis', plus other corrections and annotations, appear in another hand, in blue-black ink
- TS draft for '4. "Noise" effects'. With MS note by Hoskin, 'Another § 4 but should be included here even though incomplete. N.H.'
- TS draft, pages numbered in another hand, beginning, 'Effects of random disturbances', with AMS annotations by AMT in black ink, and in another hand in blue ink.

- AMT/C/27
Folder inscribed, 'Turing 4'. With MS note by R.O. Gandy, 'It will be difficult, in some places impossible, to know exactly what the fragments are (exactly) about.' Inside the folder is a note by Hoskin, 'I have not been able to fit in any of the following notes in the main articles. In many cases there are other notes, presumably superseded, on the reverse of these pages. Some of these are not sequential.' Many of these drafts are on the back of programme sheets for Manchester University Computing Machine Laboratory, and some carry routines related to the themes of the MSS, and perhaps intended to test them. The material is in the form of bundles clipped together, some with AMT's heading or description, and have been left as received. Includes:-

- 'Pessimum compressed hexagonal golden lattice'
- 'Half way compressible golden lattice'
- 'Golden rectangular lattice'
- 'FIRCONES. Paper theory'. Drafts, notes, and calculations
- 'KJELL Theory'. Drafts, notes, and calculations. Page 7, labelled 'NORMAST', contains a subroutine tree including a number of the subroutines described in the folder
- 'KJELL PREP TRACK PAIRS'. Drafts, notes and calculations, in ink and pencil, with many revisions and corrections. Some pages used on both sides, and some top and bottom
- notes, signed B.R. [Bernard Richards] on 'Morphogenesis of cellular structure'
- notes and calculations, with computer routine 'OUTERFIR', perhaps related to FIRCONES, and notes for modification of OUTERFIR programme
- table of flower species used by AMT for work on morphogenesis
- untitled notes, calculations and diagrams, many on lattices
- 'Naturally occurring phyllotactic patterns'
- 'Amplitude with 1 dimensional waves'
- 'Rate of change of wavelength'
- 'Measurements taken on some specimens'
- TS, 'Evidence relating to the diffusion reaction theory of morphogenesis', by C.W. Wardlaw, with MS note at head, 'Rough draft. A.M. Turing'.