Global regulations
Many shell patterns indicate that regulatory events occurred simultaneously along the whole growing edge,
indicating the involvement of a global control. Global termination of pigment production is especially frequent.
The pattern of Oliva porphyria is an intricate example, in which this global control less obvious.
From “The Algorithmic Beauty of Sea Shells”
© Hans Meinhardt and Springer-Company
Branch formation on Oliva porphyria is
based on the trigger of backwards-running waves
Branches are the dominating pattern elements on the shell of Oliva porphyria. This pattern indicates the
occasional initiation of backwards-running waves. This is unusual since after passing of a wave, the region
should be refractory for another wave. Most remarkably, many branches are formed simultaneously at distant
positions (green dotted lines)…
Branch formation by a temporary transition
into a steady state
Backwards-running waves are triggered
whenever the hormone concentration
(green) becomes too low
Model: each activated cell produce a hormone (green) that stabilizes the inhibitor (red).
When the number of waves become too low, cells remain activated until a backwardsrunning wave is triggered. Many branches form simultaneously (red dotted line )
Simulation of Oliva porphyria
Details are well described
A large non-pigmented
region can lead to
stronger pigmentations in
other regions
After the trigger of backwardsrunning waves, often an
attempt can be seen to form a
further wave running into the
original direction. A hook-like
pattern results…
…sometimes the second
wave survives, causing two
parallel lines close to each
other. The faint pigmentation
resulting from the temporary
steady state is clearly visible
(arrow)
ba
aThe systema 2is more
2a
complex: the spontaneous
initiation of new
 s

r
a

D
a
a
2
t pairs( sof

b

s
d
)
(1

s
a
)
x 2
waves
indicate
the
involvement
of a second and longb
d
a
a 2  ba
b
 s
t
1  sa a 2
n
c
 rc  ai / n
t
i 1

rb b
c
lasting
 2 c inhibitor
 Dc
x 2
 rc c
d
2d
 rd a  rd d  Dd 2
t
x
d: the long-lasting
second inhibitor
New pairs of two diverging waves are triggered
whenever the long-lasting inhibitor drops to a low level.
A very different pattern can be described by the same
interaction
Parameters are changed such that wave termination can occur
without collision whenever a certain wave density is obtained
(changed is the Michaelis - Menten constant in the action of the
inhibitor; (sb in the equation at the preceeding page).
Conclusion
A common scheme in the patterning of shells is a global control of
pigmentation. A globally distributed hormone may be the controlling
agent. Whenever the pigment density becomes too high or too low,
hormone-controlled changes of parameters may lead to global pigment
termination or to transitions from a pulse-like to a steady state
activation. In this way, an average level of pigment deposition can be
maintained. For Oliva porphyria the best fit is obtained if a hormonecontrolled change of the half-life of the inhibitor is assumed.