Physically the pore/cell size is dependent on the electric field, however the experimental variable is the applied potential. Roughly speaking, the geometry of the cell arranges itself so that the field at the base of the pore is ~1 V/nm.

There are also theories about self-organization. For example, a famous Benard's experiment - he obtained hexagonally arranged cells with circulators inside while he was heating the oil/water mixture at the bottom and cooling at the top. Hence, a gradient of a physical quantity like temperature, or a potential provides such a type of self-organization. More anwsers one can get from Kluwer's book "chemical waves and patterns" where AAOs self-organization issue one can find as a Turing pattern (Alan Turins described mathematically self-organization in stripe-like and a hexagonal typestructures).

In general, in electrochemistry a self-organization usually results in a hexagonal symmetry. This is a result of distribution of electric field lines. You can check publication of Monter-Moreno et al.

So hexagonal geometry is a result of a gradient of potential, hence the geometry of the electric field lines is a crucial factor.

PS. you can also check following publications:

D. Semwogerere, M.F. Schatz, Evolution of hexagonal patterns from controlled initial conditions in a Bènard-Marangoni convection experiment, Phys. Rev. Lett. 88 (2002) 054501

R. Kapral, K. Showalter, Chemical waves and patterns, Kluwer Academic Press, 1995

T. Leppäanen, M. Karttunen, R.A. Barrio, K. Kaski, Turing Systems as Models of Complex Pattern Formation, Braz. J. Phys., 34 (2004) 368-372

J. Randon, P.P. Mardilovich, A.N. Govyadinov, R. Paterson, Computer Simulation of Inorganic Membrane Morphology Part III: Anodic Alumina films and membranes, J. Colloid and Interface Science 169 (1995) 335-341

V.P. Parkhutik, V.I. Shershulsky, Theoretical modelling of porous oxide growth on aluminium, J. Phys. D: Appl. Phys. 25 (1992) 1258-1263

H. Asoh, S. Ono, Fabrication of ordered anodic nanoporous alumina layers and their application to nanotechnology, w: Electrocrystallization in Nanotechnology (Georgi Staikov Ed) Wiley 2007

G.H. Thompson, G.C. Wood, Anodic Films on Aluminum, Corrosion: aqueos processes and passive films, J.C. Scully (ed) Academic Press 1983

D.D. MacDonald, M. Urquidi-MacDonald, Theory of Steady-State passive films, J.Electrochem.Soc. 137 (1990) 2395-2402

G. Patermarakis, K.Moussoutzanis, Electrochemical kinetic study on the growth of porous anodic oxide films on aluminium, Electrochim. Acta 40 (1995) 699-708

J.P. O’Sullivan, G.C. Wood, The morphology and mechanism of formation of porous anodic films on aluminium, Proc. Roy. Soc. Lond. A. 317 (1970) 511-543

S. Wernick, R. Pinner, P.G. Sheasby, Anodizing of aluminium: General notes and theory w: the surface treatment and finishing of aluminium and its alloys, Finishing publications ltd. Teddington, Middlesex, (1987) England 289-368

D.H. Fan, G.Q. Ding, W.Z. Shen, M.J. Zheng, Anion impurities in porous alumina membranes: Existence and functionality, Micropor. Mesopor. Mat. 100 (2007) 154–159

D.D. MacDonald, On the formation of voids in anodic oxide films on aluminium, J.Electrochem. Soc. 140 (1993) 127-130

Thank you Stephen and Wojciech for your contribution, especially Wojciech for the long bibliographic list.

So, you both seem to agree with me that the real ruling quantity is the field E=V/s, with s gap between the electrodes. However, I've read a number of papers on anodic porous alumina, and never found anyone mentioning E as a variable on which the pore or cell size may depend. They all speak about V only, additionally giving often even an exact relationship of proportionality between pore and/or cell diameter (d or D, respectively). This is what is found on the seminal paper of Diggle, for instance, or in the various reviews by Thomson, Shingubara, etc (please take a look at my old citeulike repository, (seek userid: gurgite), they say something 1.2 to 1.5 nm/V.

Also, I myself tried once to anodize an Al foil 2x2 cm^2 that was not parallel to the (same size) Pt foil, but inclined, in such a way that at the bottom (deeper submerged point) the distance s was approx. 1/2 (around 0.5 mm) than at the top (1 cm). And expected thus, due to the factor 2 in E=V/s, that the bottom will have larger pores (double diameter), but they were approx. the same size as the pores in the top half of the Al. So? Anyone who makes EC simulations with Comsol, out there?

I also gave direct relationship between pore diameter and potential in my papers :-) For example I keep constant distance between the electrodes equal 3 cm.

Are distances between pore centers in Your experiments same for both distances? Differences in pore diameters may be implied by field-assisted pore walls chemical etching by the electrolyte, which is in deed - caused by electric field.

If the interpore distances (distances between pore centers) varied for both cases (0.5 cm and 1.0 cm) Your results are very valuable. Typically, everyone keeps constant distance between electrodes and doesn't care about it ;-)

Moreover, anodes "burning" is also caused by electric field, what is very problematic for many beginners. If any E/d valus would be optimized and reffered to the "burning" sets of parameters it would be a great contribution in this matter.

I think the issue is that you're expecting the potential to drop linearly from the Pt electrode to your anode. The anodic film is far more resistive than the electrolyte so nearly all of the drop in the potential is in the oxide, not the electrolyte. The relevant distance for calculating the field in the film isn't the distance between the electrodes, it's the thickness of the film. In a porous film, the barrier layer at the base of the pore is of (approximately) constant thickness so the electric field depends on the applied voltage.

But barrier layer thickness depends on the anodizing operating conditions.

Additionally, when electrodes are too far anode's burning is rather common.

For the first time I hear that the distance between the electrodes determines the morphological characteristics of porous alumina. All experiments show that the cell and pore size are determined solely by voltage.