RICHARDS | 387
figure 35.6 Cannocapsa stehoscopium
with twenty spines.
Reproduced from Bernard Richards, ‘The
morphogenesis of Radiolaria’, MSc Thesis,
University of Manchester, 1954, with thanks to
Dr Richard Banach. Original image taken from
Ernst Haeckel, Report of the Scientific Results of
the Voyage of H.M.S. Challenger During the Years
1873–76, Volume 18.thus defined. One needs to know where the spines are located on the sphere, and also the
diameter of the sphere and the lengths of the spines protruding from it. Normal powers of
mathematical visualization are inadequate for this task—mine certainly were—and I needed
the computer’s help.
It must be admitted, though, that in those days computers were less helpful than they are
now. The computer that I used, the Ferranti Mark I, had no facilities for a visual display output
and only a very primitive printer: this could print only numbers and alphabetic characters—not
graphics. So I decided to use some clever programming to make it print contour maps of the
surface. On the first page was displayed an array with θ taking values from 0° to 90° and φ taking
values from 0° to 360°, while on the second page the values of θ from 90° to 180° were shown;
so between them these two pages mapped both the northern and southern hemispheres of
the shape. The printer covered the pages with the arcane teleprinter symbols that Turing had
brought with him to Manchester from Bletchley Park, each one representing a distance from
the centre of the sphere (a height) on a scale from 0 to 31. Thus the whole surface of the sphere
was present on my two-dimensional sheets. I was then able to draw contour lines on the sheets,
locate the spines, and record their lengths. In this way the computer found three-dimensional
shapes corresponding to the above figures.
Comparing the computed shapes with real Radiolaria
I set my computed shapes against their closest matches from among the Radiolaria, and the
matches were very good. Figure 35.7 shows my computed shapes superimposed upon Circopus
sexfurcus (left) with two spines at the two poles and four around the equator, and on Circogonia
icosahedra (right) with twelve spines equidistantly spread over its surface. Most marvellously,
starting from nothing more than Turing’s morphogenesis equation, I had produced the shape
and surface structure of creatures that accurately matched in shape and form real Radiolaria
found in the oceans of the world.