Janus: The Papers of Alan Mathison Turing

King's/PP/AMT/C contains:
<-- See earlier
19	'The game of "Psychology"'
20	'The elliptic integrals K, E.'
21	'Précis of Relativity Theory'
22	'The rules of GO'
23	Notes and calculations
24-27	Work on morphogenesis
28	'On the Gaussian Error Function'
29	'Nature of Spirit'
30	'Treatise on the Enigma'
31	Report on AMT's visit to the Naval Computing Machine Laboratory at Dayton, Ohio
31A	'Enigma series, Volume 6, Duenna. Communications Intelligence Technical Paper TS-10/E-6'
See later -->

More information

Please feel free to contact the repository.

The Papers of Alan Mathison Turing

Title	Work on morphogenesis
Reference	AMT/C/24-27
Extent and Medium	4 envelopes; paper

Content and context

The files comprise notes, diagrams, tables, calculations, and computer routines. The material is mainly AMT's autograph manuscripts and typescripts, with many additions and corrections. 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 manuscript. Later notes or comments in the hands of Hoskin and Gandy are identified and indicated wherever possible.

These files were received from N. E. Hoskin in 1978, and are 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.

Further information

See Dr. J. Swinton's web pages http://www.swintons.net/jonathan/turing.htm for a detailed analysis of page sequences and contents.

King's/PP/AMT/C/24-27 contains:

'Morphogens. Turing I'. The folder has a manuscript note by Gandy, 'This contains consecutive pieces which were not incorporated by Hoskin and Richards in their paper'. The file includes, among other unidentified pages:-. - 'Outline of the development of the daisy', including sections on 'Considerations governing the choice of parameter' and 'Early stages in pattern formation'. The pages have been numbered by R. O. Gandy;. - a 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 gamma';. - '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.
1 envelope; paper.

1950–1959

'Morphogen. Theory of Phyllotaxis. Turing 2'. The folder has a manuscript 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. The folder includes:-. - AMT's typescript draft, with many autograph manuscript revisions, and numbered in another hand. AMT's 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 manuscript headed, 'Stability of 2nd 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.
1 envelope; paper.

1950–1959

'Chemical Theory of Morphogenesis. Turing 3'. The folder has a manuscript note by R. O. Gandy, 'Part II of draft used by Hoskin and Richards'. The file includes:-. - typescript draft, numbered in another hand. The draft is AMT's typescript, with many autograph manuscript 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. - typescript draft for '4. "Noise" effects', with a manuscript note by Hoskin, 'Another § 4 but should be included here even though incomplete. N. H.'. - typescript draft, with pages numbered in another hand, beginning, 'Effects of random disturbances', with autograph manuscript annotations by AMT in black ink, and in another hand in blue ink.
1 envelope; paper.

1950–1959

'Turing 4'. The folder has a manuscript 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 manuscripts, 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. The file 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 have been 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';. - typescript 'Evidence relating to the diffusion reaction theory of morphogenesis', by C.W. Wardlaw, with manuscript note at head, 'Rough draft. A.M. Turing'.
1 envelope; paper.

1950–1959