Sep 13


apomorphism (n) The false belief that evolutionary novelty is good in and of itself, that some novelties are so special that they trump all others, and that the organisms possessing these special novelties are superior in some way to all organisms lacking them. See also: egotism, mammalocentrism, ‘scientific’ racism

Cycas thouarsii and Ginkgo biloba [CC-BY-SA-3.0 Steve Cook]

— “So I was just chatting with the guy – our saplings are in the same nursery – and all of a sudden he comes out with ‘So, what’s it like being a living fossil?’ And obviously the look on my caudex is all What The Actual Fuck, but he just ploughs on regardless, and doubles down with ‘Primitive, I mean, that’s the word, isn’t it?’ – and I just transpire in horror.”

— “He actually used the ‘P’ word? That’s our fucking word, he cannot use that word! Hears some fern prothallus reclaiming it and thinks it’s OK for him to say it.”

— “IKR? So I call him out on his apomorphist attitude, and he gets all huffy. Thinks just because he’s not calling mosses Lower Plants to their sporangia, and throwing herbicide at quillworts on the street, that everything is fine and that people actually give a fuck about an endangered cycad when there’s some orchid to rescue instead. ‘They plant ginkgos everywhere now, so what’s the problem?’, like this place isn’t still London planes as far as the eye can see, dropping their fruit wherever the hell they like. The minute you drop a few seeds, everyone’s moaning about the stink.”

— “That’s fruit-privilege right there. They don’t even see it, do they?”

— “Preach. But his sap’s all rising now, and he just *Will Not Let It Lie*: starts banging on about how some of his best mates are basal, and his wife is an Amborella, and that he just doesn’t see seed-wrapping, because “we’ve all got seeds underneath”. Like liverworts don’t exist! I just totally lost my cones at that point and had to walk away before I punched the lenticel-hole right in the anthers.”

— “Jeez, Angiosperms can be such ignorant dicks.”

Jul 07

Stems all the way down

In the days when potted plants were more than just disposable land-filler, my Nan would try to force her wizened poinsettia to flower by sticking it into a bin-liner with some apples every night from October until December. Sum total of flowers she ever saw: zero. Ho hum. But how many poinsettia flowers can you see in the picture below?

Euphorbia pulcherrima [PD, USDA Scott Bauer]

Poinsettia (Euphorbia pulcherrima)

If you’re wondering whether you can include the ones that are partly off-screen, you are asking the wrong question. There are many hundreds of flowers here, not six or ten. The red leafy-looking things you might have been cruelly mislead into thinking were petals are actually brightly coloured leaves. The flowers themselves are found in the tiny yellow-green blobs in the middle…

Euphorbia pulcherimma cyathia [CC-BY-SA-2.5 André Karwath]

Poinsettia cyathia [CC-BY-SA-2.5 André Karwath]

…but they are not – as it turns out – the blobs themselves. Each one of those blobs is itself a bunch of tiny petal-less flowers: one petal-less female flower, and a bunch of tiny petal-less male flowers consisting of just one anther each. This structure – a cyathium – is found in all the species of Euphorbia, the genus to which the poinsettia and 2000 other species of spurge belong.

Cyathium [CC-BY-SA-3.0 Ies, Aelwyn]

Cyathium of a different species of Euphorbia, but showing the single female flower, and here two males flowers [CC-BY-SA-3.0 Ies, Aelwyn]

In one of the close relatives of the poinsettia – the crown-of-thorns – two coloured leaves surround just a single cyathium, making it a flower-squared: a bunch of tiny flowers masquerading as a single bloom:

Euphorbia_milli [CC-BY-SA-3.0 Ezra Katz]

Eight crown-of-thorns cyathia [CC-BY-SA-3.0 Ezra Katz] – as the author says on the upload page on Wikipedia “a close up of Euphorbia milli cyathia (not of the flowers!)”

This means that the poinsettia ‘flower’ is really a flower-cubed: it is a set of tiny petal-less flowers grouped together into a cyathium, and then a bouquet of cyathia are grouped together and surrounded by coloured leaves. It is a flower reinvented – twice!

The cyathium is one of many re-invented wheels in the business of making flowers. All the 33 thousand species in the daisy family have flowers-squared, as do all of the arum lilies. The flowering structures of grasses are flowers-squared or cubed according to taste.

Silybum marianum [CC-BY-SA-4.0 Steve Cook]

Thistles (like this Silybum marianum) and all the other daisy family have flower-heads that are composed of many very small flowers clustered together and – in this case – surrounded by spiky rather than ‘pretty’ leaves.

Deeper down the rabbit-hole…

When I said the ‘red leafy-looking things’ on a poinsettia weren’t really petals, I wasn’t lying, but from an evolutionary point of view, that’s all a petal actually is. Petals are a ring of leaves that became useful for attracting pollinators in some long-dead ancestor of the flowering plants.

Something similar applies to the male anthers and female carpels at the centre of a flower: these are also modified leaves, wrapped around the tissue that makes the pollen and egg-cells. So even a single real flower can be seen as a cluster of smaller male and female ‘florets’ (botanists call these sporangia), themselves made of rolled leaves, and surrounded by yet more (prettily coloured) leaves. A flower is a leaf-squared, so a poinsettia ‘flower’ is a leaf-to-the-fourth-power.

Liriodendron tulipifera [CC-BY-SA-.4.0 Steve Cook]

Tulip-tree magnolia (Liriodendron tulipifera) – some pretty leaves wrapped round some sexy leaves

Oh, but we’re not done yet.

What is a leaf? Well, if you hold up the leaf of most land plants to the light, you’ll see a lot of veins. Depending on what you’re looking at, these may be arranged in neat parallel lines, or in a tree-like branching network.

Cotinus coggygria [CC-BY-SA-4.0 Steve Cook]

A tree within a tree (Cotinus coggygria)

The latter kind gives you a clue as to what a leaf really is. A leaf is a much-branched but flattened stem with tissue stretched out across it like the webbing between the toes of a duck.

So if a leaf is a stem-squared, then a poinsettia ‘flower’ is a stem-to-the-fifth-power:

  • Start with a stem
  • Group a bunch of stems together with some webbing to make a leaf
  • Group a bunch of reproductive leaves together with some pretty leaves to make a flower
  • Group a bunch of simplified flowers into a cyathium
  • Group a bunch of cyathia together with some pretty leaves to make a poinsettia

Plants: what you get when you take one good idea and run with it for 500 million years.

Apr 13

More botanical baggings

Previously on Bagging Botanic Gardens: Wisley, Brussels, Down House, Much Else Besides.

Eden Project

An old clay pit in Cornwall doesn’t sound like the most promising place to find a tropical forest, but the alleged proximity of the entrance to Magrathea might go some way to explaining it. The Eden Project’s bubble-wrap domes are now such a familiar part of the Cornish tourist board’s marketing that you’re not really expecting them to be as impressive as they actually are in the flesh:

Eden Project [CC-BY-SA-4.0 Steve Cook]

The domes are made of plastic. The left side houses a tropical biome; the right Mediterranean.

Inside the tropical biome there is a tree-top walkway that takes you up a stairway suspended in mid-air to a platform suspended in the same. This platform sways from side to side at the exact resonant frequency of the human bowel. There was probably a view. I don’t really recall.

Eden walkway [CC-BY-SA-4.0 Steve Cook]

Stairway to heaven. One way or the other.

As it was the depths of winter when we visited, there was not all that much happening outside in the Cornish biome, but the clean air and high humidity supports a lush growth of mosses and lichens on every available surface.

Eden lichens [CC-BY-SA-4.0 Steve Cook]

Tickets are a breath-taking £25+ per person, and I should imagine pre-booking is sensible in the summer months.

Botanerd highlights: my memory is terrorised, fragmentary. Some palms. Definitely some rubber trees. Jewelled crabs?

Westonbirt Arboretum

On the way back from Cornwall, we dropped in at the national arboretum in Westonbirt, which is run by the Forestry Commission. We’d been there once before for a wedding, but hadn’t had much time to explore the grounds. As previously noted, it was the depths of winter, so quite a lot of the trees were dormant, and my photo-roll is a bit scant. However, there are several areas planted heavily with conifers, so I spent a happy couple of hours running about trying to find fallen cones to add to my collection. I would pay good money for the cone of a Taiwania cryptomerioides (seriously – call me), but – in keeping with most of specimens of this species in the UK – Westonbirt’s coffin tree was far too young to have any. Oh well.

Taiwania cryptomeroides [CC-BY-SA-4.0 Steve Cook]

Taiwania cryptomerioides, the coffin tree

Tickets are £15.

Botanerd highlights: trees. Lots and lots of trees. If we’d timed it better, I would have the pretty pictures to wax lyrical about the 79 ‘champion’ trees they have, which are the biggest of their species you can find in the UK. But it was too bloody cold, so I shan’t.


In pre-emptive defence, Las Canarias = winter sun ∩ not-imprisoning-the-gays ∩ relative affordability.

Eschewing the fleshpits of the Yumbo Centre, we walked for mile after sweaty mile under the very sun we had paid to enjoy, to the Botanic Gardens of Maspalomas. Only to find that Epiphany is still a thing on Gran Canaria, and so a glimpse through some locked gates was all we were likely to get:

Maspalomas botanic gardens [CC-BY-SA-4.0 Steve Cook]

Jesus says “no”

Never one to let an unlikely man-god get in my way, we tried again on the morning of our flight home. The gardens are all outdoors, and showcase sub-tropical plants, including a number of the Canary Islands’ wide range of endemics. The Canary Island spurge – which looks like a cactus but isn’t – is everywhere on Gran Canaria, and looks absolutely gorgeous in the sunshine. The photo below is not at high enough resolution for you to see that is it also covered in spider webs. Hundreds and hundreds of them, each with an attendant angry arachnid. The stuff of nightmares. Yours obviously, not mine. My nightmares are wholly taken up with falling to my death from great heights.

Euphorbia canariensis [CC-BY-SA-4.0 Steve Cook]

Canary Island spurge (Euphorbia canariensis)

Entry is free! In addition to the botanic gardens, the Paseo los Gatos Rabiosos (officially, the Paseo Costa Canaria, and Calle las Dunas) have some pretty nice planting along them, including a lot of Norfolk Island pines (actually monkey-puzzles), none of which – tragically – had cones within scrumping distance. The latter street also takes you to the edge of the amazing dune system and nature reserve behind the beach.

Araucaria heterophylla [CC-BY-SA-4.0 Steve Cook]

Araucaria heterophylla, the Norfolk* Island Pine**. *Nowhere near Norfolk. **Not a pine.

Botanerd highlights: along with the native spurge, the Madagascan traveller’s ‘palm’ Ravenala is the Maspalomas go-to for generic corporate planting. However, the one at the botanic gardens was considerably more majestic than most of the hotel frontage offerings.

Ravenala madagascarensis [CC-BY-SA-4.0 Steve Cook]

If you’re trying to work out how Ravenala madagascarensis ends up looking like this, think of it as a neatly flattened banana plant growing on top of a palm-tree trunk and see if that helps.

Wakehurst Place

We timed this final UK visit a bit better. Wakehurst is the country outpost of Kew Gardens, and home to the Millennium Seed Bank, which aims to preserve the seeds of 25% of the world’s seed plants by 2020.

Fritillaria meleagris [CC-BY-SA-4.0 Steve Cook]

Snake-head fritillaries (Fritillaria meleagris)

Being a contrary dick, I went hunting for plants that don’t bear seeds to photograph. Here is Cthulhu escaping from R’lyeh.

Osmunda regalis [CC-BY-SA-4.0 Steve Cook]

Royal ferns (Osmunda regalis) – crosiers grasping for your soul

And some mosses: diploidy is for wusses.

Wakehurst mosses [CC-BY-SA-4.0 Steve Cook]

Mosses. I really need to put my money where my mouth is and go on a bryophyte identification course.

Tickets are £12.50, but factor in an unexpected £10 for the car-park too, unless you fancy a 6 mile walk (or a once-every-two-hours bus) from from Haywards Heath railway station.

Botanerd highlights: the huge stand of royal ferns above are reason enough alone to visit, but Wakehurst’s pinetum also has some interesting species: Keteleeria evelynianawhich I’ve seen nowhere else before, and a lot of small firs which have beautiful immature cones with brightly coloured bract scales at this time of year.

Abies squamata [CC-BY-SA-4.0 Steve Cook]

The flaky fir (Abies squamata). Lovely cones. Dreadful branding.

Jan 04

Modular origami

A few months ago, I went to a creative origami lunchtime session organised by some lovely people at $WORK. I’d done origami a bit when I was younger, but mostly just frogs and cranes, which have since helped me while away the hours when invigilating exams. However, at this lunchtime session I was shown how to make modular origami. This involves making lots of (generally quite simple) origami parts, and then slotting them together to make larger structures.

Sonobe origami assembly [CC-BY-SA-3.0 Steve Cook]

I went home with a simple 12-unit Sonobe ball that afternoon and was very pleased with myself.

Cumulated octadedron (sonobe) [CC-BY-SA-3.0 Steve Cook]

Entry-level modular origami: the 12-unit Sonobe ball. Mathematically, it’s a cumulated octahedron; practically, it’s 12 sheets of square paper and about 1 hour of your time.

Things have rather escalated from there.

Assorted modular origami [CC-BY-SA-3.0 Steve Cook]

Between running some of these lunchtime sessions myself now, and being asked on several occasions on Twitter about how I make the pretty things I keep tweeting, I thought it’d be useful to put together a quick guide (or a link-farm, at least)..

Sonobe units are very easy to fold, quite forgiving, and can be used to make a cube (6 units), a cumulated octahedron (12 units), a cumulated icosahedron (30), and a kind-of truncated icosahedron (90, basically a spiky football). They’re a pretty good introduction to the general principles:

Assorted (sonobe) [CC-BY-SA-3.0 Steve Cook]

Sonobe family: 90, 30, 12, 6 and 3 units. The 3-unit one is a trigonal bipyramid but barely counts! These have all been made with the slightly modified unit mentioned below. The 90 units one is the biggest Sonobe that’s really worth making IMHO: about 3 hours’ work

The 30-unit ball has the symmetries of an icosahedron (or dodecahedron). Once you’ve learnt how to construct that object in Sonobe modules, you’ve essentially learnt how to construct any 30-unit modular origami ball: they mostly involve slotting 30 edge-units into groups of three to form the 12 pentagonal faces of a dodecahedron (or equivalently/alternatively, slotting them into groups of five to form the 20 triangular faces of an icosahedron – the difference is mostly one of perspective).

Cumulated icosahedron (sonobe) [CC-BY-SA-3.0 Steve Cook]

Cumulated icosahedron made of Sonobe units: 30 sheets of paper, and – if you’ve got the hang of the 12-unit ball – still only 1 hour of your time

There are lots of variations on the Sonobe unit you can (re)invent, by adding back-folds that expose the other side of the paper, or that make the tabs narrower than the pockets, giving a more intricate look.

Cumulated icosahedron (sonobe variant) [CC-BY-SA-3.0 Steve Cook]

Cumulated icosahedron made of slightly modified Sonobe units

Although the 90-unit structure is quite stable, the next one up (270 units) tends to sag under its own weight over time, but by that point it felt like a right of passage to make one.

270 (sonobe colourchange) [CC-BY-SA-3.0 Steve Cook]

9 hours construction, plus some planning. This uses duo paper, which is coloured on both sides, and a modified Sonobe unit that has a reverse fold to expose the other side of the paper in each module.

The Sonobe units can also be assembled inside-out to make inwardly cumulated polyhedra…

Cumulated postive negative icosahedra (sonobe) [CC-BY-SA-3.0 Steve Cook]

Getting the last few units in on the inverted ball (left) is tricky.

…and they can also be assembled in pairs and then assembled into a spiked pentakis dodecahedron...

Pentakis dodecahedron (sonobe colourchange pairs) [CC-BY-SA-3.0 Steve Cook]

Pentakis dodecahedron, with a reverse-fold Sonobe unit that shows the other side of the paper.

…and other structures.

Rhombic triacontahedron (sonobe colourchange pairs) [CC-BY-SA-3.0 Steve Cook]

The site above describes this as a rhombic triacontahedron, but I’m pretty sure it isn’t. I’m not sure what it actually is though. Has both colour-change and the units are assembled ‘inside out’ to make it inwardly cumulated.

The next unit I tried was the Penultimate edge unit (attributed to Robert Neal), which can be used to make a wireframe dodecahedron, as demonstrated by Matt Parker, the stand-up mathematician. Other variations of this subunit can be used to make pretty much any other wireframe polyhedron.

Dodecahedron (penultimate) [CC-BY-SA-3.0 Steve Cook]

Dodecahedron. I was trying to use up the boring coloured paper on this one, but I quite liked the result in the end!

Thomas Hull’s PhiZZ edge unit makes similar wireframe structures, but the modules fit together more tightly and the resulting structures are much more robust than you get with the penultimate modules.

Truncated icosahedron (phizz) [CC-BY-SA-3.0 Steve Cook]

Truncated icosahedron – this is basically the shape of a football (12 pentagons, surrounded by hexagons) and of some viral capsids too.

You can also make colour-change variants using the technique shown in Lewis Simon’s decoration boxes.

Dodecahedron (phizz colourchange) [CC-BY-SA-3.0 Steve Cook]

Dodecahedron made from PHiZZ units with a colour-change.

For structures based on dodecahedra/icosahedra and made from edge-units, you can always get away with using just three colours and never have two of the same colour pieces touching. This is because you can draw a Hamiltonian circuit on a dodecahedron: that is a path from vertex to vertex that only visits each vertex once, and which comes back to where it started. You can represent this in 2D on a Schlegel diagram.

Hamiltonian circuit through a dodecahedron [CC BY-SA 3.0 Tomruen/Steve Cook]

Hamiltonian circuit through the Schlegel diagram of a dodecahedron [CC BY-SA 3.0 original by Tomruen, modified by Steve Cook]. The red and purple edges form the Hamiltonian circuit; the grey edges are what is left over. You’ll notice that every vertex has one of each of the three coloured edges. The diagram is a projection of a dodecahedron: imagine taking a wireframe of the dodecahedron and shining a torch through it: the Schlegel diagram is the 2D shadow this 3D polyhedron casts on the wall. It’s fairly easy to work out which edge in the 2D diagram correspond to which edge in the thing you’re building.

If you colour alternate edges of the Hamiltonian circuit in two of your chosen colours, and the rest of the edges in the third, then you’ll avoid having any colour-clashes. I only learnt this after I started making these structures, so not all of them have this optimal colouring! The same 3-colour rule is true for the other Platonic solids, and also for the truncated icosahedron.

Francesco Mancini’s star-holes kusudama uses a similar module to the PHiZZ, but with a little back-bend that gives a nice 3D star effect. This one is a dodecahedron-shaped (30 units), but a 90-unit truncated icosahedron should also be possible.

Star holes dodecahedron [CC-BY-SA-3.0 Steve Cook]

Star-holes dodecahedron.

UPDATE: yes, it is possible 🙂

Star-holes truncated icosahedron [CC-BY-SA-3.0 Steve Cook]

Star-holes truncated icosahedron

Lewis Simon and Bennett Arnstein’s triangle edge unit can be used to make very nice patchtwork tetrahedra, octahedra and icosahedra.

Icosahedron (triangle edge) [CC-BY-SA-3.0 Steve Cook]


They’re a bit fiddly to put together but are very robust once constructed. A similar patchwork effect for the dodecahedron can be achieved with M. Mukhopadhyay’s umbrella module; Sonobe units can be used to make analogous Battenberg-cake style cubes.

Assorted (triangle edge sonobe umbrella) [CC-BY-SA-3.0 Steve Cook]

Battenberg-cake Platonic solids. The dodecahedron is made from umbrella units; the cube from Sonobe. The tetrahedron, octahedron and icosahedron are all made from triangle edge modules.

The simple isosceles triangle unit (attributed variously to M. Mukhopadhyay, Jeannine Mosely and Roberto Morassi) can be used to make small and great stellated dodecahedra.

Small and great stellated dodecahedron (isosceles) [CC-BY-SA-3.0 Steve Cook]

Great (left) and small (right) stellated dodecahedra.

The small stellated dodocahedron is particularly pleasing and makes a fairly robust decoration if made of foil-backed paper.

Small stellated dodecahedron (isosceles) [CC-BY-SA-3.0 Steve Cook]

Xmas decs

The great stellated dodecahedron can be made from the same subunit, but is tricker to construct because a tab has to curl around into a pocket that is partly inside the next tab round. I used needle-nosed forceps to construct this, and I’m still not terribly happy with the result.

The opposite is true for Paolo Bascetta’s star module, which makes a great great stellated dodecahedron, but a rather *eh* small stellation. This module needs duo paper (i.e. paper that is coloured on both sides) for best effect.

Small and great stellated dodecahedron (star) [CC-BY-SA-3.0 Steve Cook]

Great (left) and small (right) stellated dodecahedra.

Dave Mitchell’s Electra module can be used to make a icosidodecahedron: it’s unusual in that each module corresponds to one vertex of the structure: the edge units described up to this point combine together to make each vertex.

Icosidodecahedron (electra) [CC-BY-SA-3.0 Steve Cook]

Icosidodecahedron made from Electra modules

I’m not that happy with my Void kusudama (Tadashi Mori): I should have used duo paper, but it was really tricky to put together. Maybe one day. It’s one of the few structures here that is back to the original octahedral/cubic 12-unit structure. I’m not sure the 30-unit version would be stable.

Octahedral void [CC-BY-SA-3.0 Steve Cook]

Octahedral void

UPDATE: Yeah, I don’t think the 30-unit version is do-able. I think the units are too wide to actually fit into an icosahedron: I couldn’t even manage it with glue, so I don’t think it’s just a stability issue. However, I did do a better 12-unit version, with duo paper and a little reverse fold on the outer edge to expose the second colour properly, which I’m quite pleased with:

Octahedral void (modified) [CC-BY-SA-4.0 Steve Cook]

Octahedral void (modified)

Tomoko Fusè’s little turtle modules are extremely flexible: they can be used to make pretty much any polyhedron that is made of regular polygons. However, because the flaps are only one paper layer thick, they don’t fit together terribly tightly, so I’ve only found them robust enough to make smaller structures without the help of glue. However, with glue, I’ve made a rhombicosidodecahedron, which is cool because it is built of pentagons, triangles and squares (all of the polygons found in the Platonic solids)…

Rhombicosidodecahedron (little turtle) [CC-BY-SA-3.0 Steve Cook]

The impossible-to-spell rhombicosidodecahedron.

…and also a pair of snub-cubes, which are even more interesting as the snub-cube has two non-superimposable mirror images, like hands, amino acids and amphetamines.

Snubcubes (little turtle) [CC-BY-SA-3.0 Steve Cook]

Snubcubes: left- and right-handed enatiomorphs.

I found Maria Sinayskaya Etna kusudama in Meenakshi Mukerji’s Exquisite Modular Origami book. It’s a really pretty model, and robust once it’s assembled, but it can be a bit fally-aparty during construction: I used very small clothes pegs to hold it together as I was making it.

Etna kusudama [CC-BY-SA-3.0 Steve Cook]

Etna kusudama.

Dennis Walker’s compound of five octahedra is also a bit fally-aparty, but I like it as – unlike many of these models – it genuinely is the polyhedron so-named, rather than something where you have to squint at the holes in the wire-frame and imagine faces there.

Compound of five octahedra [CC-BY-SA-3.0 Steve Cook]

Compound of five octahedra. You can easily see the yellow octahedron here: the sixth spike is underneath the model; the other four colours are similarly interlaced.

The five intersecting tetrahedra are actually a lot easier to make than they look. Francis Ow’s 6-degree modules themselves are easy to fold, and the vertices are a lot more robust than they might appear. The most difficult bit is getting the modules interlinked in the right way. I’ve managed it twice, but only whilst staring at the YouTube video and performing assorted “purple = green” gymnastics in my head.

Compound of five tetrahedra [CC-BY-SA-3.0 Steve Cook]

Compound of five tetrahedra – party piece.

Michał Kosmulski’s page has lots of lovely illustrations, instructions and inspirations. I found Tung Ken Lam’s blintz icosadodecahedron (also credited as Francesco Mancini’s  UVWXYZ intersecting planes model) there. It has the same symmetry as the Electra icosadodecahedron above, but you can see the six intersecting pentagons more clearly. Both have the same underlying structure as the Hoberman sphere – that expanding/contracting plastic stick model thing beloved of science fairs.

UVWXYZ intersecting plane icosadodecahedron [CC-BY-SA-4.0 Steve Cook]

UVWXYZ intersecting plane icosadodecahedron

This last one is a bit of a cheat as (in theory, and mostly in practice too) the structures above are held together by nothing more than friction. Valentina Gonchar’s revealed flower star kusudama has to be glued, which is kind-of cheating, but I couldn’t resist as it is two structures in one:

Flower star [CC-BY-SA-3.0 Steve Cook]

Revealed flower star – shut (left) and popped open (right).

Things I’d still like to do:

  • Build a much larger PhiZZ ball (270 units): this would be useful for demonstrating the structures of viral capsids. UPDATE: Done!

270 PHiZZ knolled parts [CC-BY-SA-3.0 Steve Cook]


270 PHiZZ [CC-BY-SA-3.0 Steve Cook]


  • I’ve not yet found a good great dodecahedron model: they exist on Pintrest, but I’ve yet to find any instructions for one.
  • I have lost wherever it was I found the instructions for this inwardly cumulated rhombic triacontahedron: I’d quite like to rediscover them so I can credit the inventor! UPDATE: this isn’t where I originally saw it, but AresMares by Gewre has a video tutorial.
Rhombic triacontahedron [CC-BY-SA-3.0 Steve Cook]

Rhombic triacontahedron of unknown source.

  • Invent my own module 🙂

May 19

Organism of the week #31 – Tardigrades

Tardigrades make me squee. These little relatives of the arthropods and velvet-worms are found in the water around mosses, and they are quite easy to find if you have a cheap microscope and a little patience. Like spiders, they have eight legs, but unlike the legs of a spider, they’re plump and stumpy, and end in the little ‘fingers’ you can just about make out in the photos below. Ignoring the excess of legs, it’s easy to see why they’re sometimes called water-bears.

One of my first-year undergrads spotted this one in a sample of moss I pulled out of the down-pipe from my bathroom. The fact that my skin flakes and spittle contributed in some small way to this microteddy’s food-chain makes me feel about as paternal as it is possible for me to feel.

Tardigrades [CC-BY-SA-3.0 Steve Cook]

May 19

Organism of the week #30 – Sticky situation

All science is either physics or stamp-collecting.

This rather mean-spirited dismissal of chemistry and biology as “stamp-collecting” is attributed to Ernest Rutherford, the physicist usually (not wholly fairly) credited with discovering the atomic nucleus and the proton.

Shortly after Rutherford’s death in 1937, particle physicists discovered the muon, pi mesons, kaons, the electron neutrino, the anti-proton, the lambda baryon, xi cascades, and sigma baryons. It took physicists the thirty years following Rutherford’s death to make sense of this veritable album of subatomic stamps.

Nature has a sense of irony, but its comic timing needs work.

There’s nothing wrong with stamp-collecting. Science very often begins with stamp-collecting, because it’s only once you have enough stamps that you can start reliably identifying patterns in the stamps, and – from there – finding the interesting exceptions and edge-cases:

Baryon supermultiplet [CC-BY-SA-3.0 Studzinski.daniel]

Subatomic particle stamp-album [CC-BY-SA-3.0 Studzinski.daniel]

I have been an on-off collector of carnivorous plants since I was very little. Most of them attract insects, kill them, digest them to tasty soup, and then absorb that soup. The soup contains useful nutrients that are missing from the soil in which they are rooted, so this helps them grow and set more seed. But there are many plants that tick some of these carnivorous boxes, but not all of them. Roridula is one I’ve blogged about before: it subcontracts out the digestion part of the process to an assassin bug. Another plant that walks the line is a kind of passionflower:

Passiflora foetida bud [CC-BY-3.0 Alex Lomas]

Passiflora foetida bud

The charmingly-named stinking passionflower bears sticky hairs on tentacle-like growths around its flower buds. There is some evidence to suggest that these help protect the flower bud from hungry insects while it develops. Similar sticky hairs are also thought to protect the flower buds of a number of other plants.

The stinking passionflower kills insects, and even appears to digest them, but it doesn’t benefit from the nutrients this releases. However, it does benefit from not having its flowers damaged by herbivorous insects. This presumably means it sets more seed, so the ultimate effect – more baby plants – is the same as for ‘true’ carnivory.

Passiflora foetida flower [CC-BY-3.0 Alex Lomas]

Passiflora foetida flower. The reason these plants are called passionflowers is because the various parts of the flower are supposed to look like hammers, nails and a crown of thorns – items associated with the Passion (crucifixion) of Jesus – rather than the earthly passions you might have been considering

Is this plant carnivorous or not? Well, whether you ultimately choose to paste this stamp into the carnivorous plant album or not is very much less interesting than the reasons you have for making that decision. I’m just glad that someone discovered this particular stamp and took the care to stick it somewhere for us to study. Here’s to collectors and taxonomists, the unsung heroes of biology.

May 05

Adaptations evolve in populations

Organisms evolve adaptations to increase their fitness

There are few ideas in science that explain as much of the natural world as does natural selection, but there are few ideas in science that are more frequently misunderstood.

Often the misunderstandings are deliberate or disingenuous, but I’ve seen quotes like the one above even in undergraduate essays and popular science books.

There are two subtle problems with what is written above.

Firstly, adaptations do not evolve in individual organisms, because evolution isn’t something that happens to individual organisms. Evolution is something that happens to populations over time. A mutation that predisposes pea plants to making flowers that are purple will initially arise in a single, particular plant cell. But only if this plant’s offspring prosper (at the expense of peas with differently coloured flowers) will the population as a whole change over time.

Adaptations like flowers that attract pollinators – and the mutations that underlie them – arise in particular individuals, but they can only become more (or less) common in populations considered as a whole. Individuals mutate, but only populations evolve.

Biologists usually think of evolution as the change in frequency of an allele in a population over time. An allele is one of the various forms a particular gene can take. In the peas studied by Gregor Mendel, flower colour was determined by a single gene, which came in two variants: one variant – one allele – resulted in purple flowers, the other allele resulted in white flowers.

If – perhaps – the purple flowers were more attractive to pollinators like bees than the white, then the purple-flowered peas would tend to be fertilised more often, and would leave more offspring. The next generation of pea plants would then inherit a larger proportion of alleles causing purple flowers, and a reduced proportion of alleles causing white flowers. The purple allele would therefore increase in frequency at the expense of the white, and the population as a whole would become more purple over time.

Pisum sativum (white) [CC-BY-SA-3.0 Rasbak]

White-flowered peas (Pisum sativum) [CC-BY-SA-3.0 Rasbak]

Pisum sativum (purple) [CC-BY-SA-3.0 Rasbak]

Purple-flowered peas (Pisum sativum)  [CC-BY-SA-3.0 Rasbak]

For similar reasons, fitness is not a property of individual pea plants either; it is an average property of purple-flowered peas versus white-flowered peas. Any particular purple-flowered pea plant might get trampled by a cow and produce hardly any pea-pods; any particular white-flowered pea plant might get lucky and find itself in a cosy, well-fertilised spot near a beehive. But on average, the purple-flowered plants will do better and they will bequeath their purple-flower alleles disproportionately to the next generation: that is what we mean by the purple-flowered plants being ‘fitter’.

The second problem with the original statement is actually the smallest word: it’s that seemingly insignificant ‘to’. That ‘to’ is short for ‘in order to’, and there’s the rub. ‘In order to’ implies teleological agency and long-term purpose, which are not properties that you can reasonably attribute to natural selection.

Natural selection is a mindless algorithm, not a purposeful process. In essence natural selection is just this:

  • Organisms vary, and some of that variation is inheritable. Some peas have purple flowers, some have white, and this is (partly) due to purple- and white-flowered peas having different alleles of a particular flower-colour gene.
  • More offspring are produced than can survive and reproduce, so they will compete, and some variants will – on average – have greater success at making offspring than others. Pea plants produce more offspring peas than are ever likely to germinate, grow and get fertilised themselves. Some variants in the offspring may be better at competing for light, nutrients or pollinators: e.g. some flower colours may be more attractive to pollinators than others.
  • Those variants will contribute disproportionately to the next generation, and the frequency of their alleles will increase over time. If the purple-flowered peas are more attractive to pollinators, they will get fertilised more often, and contribute a larger number of seeds into the next generation. These seeds – and the plants that germinate from them – will inherit their parent’s purple-flower alleles, so we will see an increasing proportion of purple flowers as the generations tick over.
  • Rinse, repeat.

The match between the purple flowers and the purple preference of pollinators strikes us as clever and sensible and non-random, and it is all those things. But the process of natural selection that created this apparent design is just the mindless consequence of variation, heredity and differential reproductive success: it has no goals, no aims, no purpose.

Equally, this is a passive process for the pea population: they are subject to evolution by natural selection, but they are not active participants in the process.The peas do not strive supernaturally to make more purple flowers. The peas do not get magically instructed by the bees to make purple flowers. The peas certainly do not know what DNA sequences they would need to invent in order to make their flowers purple: new flower-colour alleles arise by mutation, which is just as mindless as natural selection, and even more heedless of what might be useful.

Populations do not evolve in order to do anything. Populations evolve, period. Purple flowers arise and become more common in pea populations because purple flowers happen to be attractive to bees; peas do not choose to evolve purple flowers in order to attract more pollinators. Mutation just throws up new alleles, and natural selection (and other important processes) make them more or less common over time.

It can become tedious describing this process passively and long-windedly every time: “purple flowers have become more common in the pea population because flower colour is highly heritable, and purple flowers are fertilised more frequently by bees”. If you want to write this more succinctly, you could say “purple flowers have evolved in peas because purple flowers are more attractive to bees” without loosing too much meaning.

Unfortunately, you might well see someone reword this as “peas have evolved purple flowers because bees prefer them”. This isn’t exactly wrong, but the ‘have evolved’ makes it sound very much like the peas are doing something actively, rather than having something done to them passively, and it’s all too easy to interpret this phrasing incorrectly. This puts us on the slippery slope to misconception.

If this is then reworded further to “peas evolved purple flowers to attract bees”, it sounds very much like like peas are active players in the process, and that they have a long term plan of improving their attractiveness to bees. This is almost guaranteed to mislead, unless you have your evolutionary biology filter turned up to maximum.

Do not write:

Some species evolved an adaptation to do some task

Write this instead:

An adaptation that does some task evolved in [a population of] some species

Given human nature (particularly on this subject), some people will still misinterpret your meaning, but at least you’re not implicitly misleading them with your language.

Jan 08


Recursion [CC-BY-SA-3.0 Steve Cook, Andreas Thomson, Frank Vinzent]

Recursion [CC-BY-SA-3.0 Steve Cook, Andreas Thomson, Frank Vinzent]

Jan 07


Bark [CC-BY-SA-3.0 Steve Cook]

Top left to bottom right: Betula utilis var. jacquemontii, Pinus sylvestris, Prunus serrula, Pinus pinaster, Quercus suber, Araucaria araucana, Metasequoia glyptostroboides, Pinus bungeana, Betula ermanii × pubescens, Pinus nigra ssp. laricio, Betula albosinensis cv. Red Panda, Platanus × acerifolia.

Jan 06

Wisley in Winter

It’s not really a botanic garden, but the Royal Horticultural Society’s gardens at Wisley is near enough as makes no difference. We visited in what should have been the dead of winter, but which in reality was this weird sprautumn mash-up that is now December in the UK. The heather garden was particularly pretty, despite the wind:

RHS Wisley heather garden [CC-BY-SA-3.0 Steve Cook]

RHS Wisley heather garden

At £12, the entry price is a bit steep: even Kew does reduced rates when most of the plants are underground, sleeping off the summer’s excesses.

Botanerd highlights included the biggest pine-cone I have yet added to my collection (yes, it is a collection, not a sickness)…

Pinus × holfordiana cone [CC-BY-SA-3.0 Steve Cook]

Holford pine (Pinus × holfordiana) cone – nothing satisfies like a 12 inch Pinus

…and the – apparently legal – purchase of class A drugs from the attached garden centre:

Lophophora williamsii [CC-BY-SA-3.0 Steve Cook]

Peyote cactus (Lophophora williamsii)

From what I gather, owning a peyote cactus is legal in the UK unless you ‘prepare it for consumption’, which magically transforms it into a 7 year jail term. This presumably includes accidentally letting it die and dry out into a button whilst on holiday. I may be having a teesy bit of buyers’ regret.

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