Snails IV

While the visualization approaches discussed for snail-like structures so far only allow to visualize snails produced from bodies of a certain (sphere-like) geometry, here I try to introduce a method suitable for almost any geometry. Let us start with a yellow blob of a random geometry, which is surrounded (in the x-y-plane) by a belt of closely attached disks.

Building a shell I

Building a shell I

We can produce more of these spheres and combine them into a blob:

Building a shell II

Building a shell II

The yellow blob can be swept along a logarithmic spiral (and scaled accordingly) this way producing a snail-like structure.

Building a shell III

Building a shell III

To visualize the shell structure of such a body, the red blob-ring is swept along this path and also scaled accordingly.

Building a shell VI

Building a shell VI

We still have to avoid overlapping structures (which is not too difficult) and we have a nice shell structure.

Building a shell V

Building a shell V

This principle can be used for bodies of various geometry.

Building a shell VI

Building a shell VI

As demonstrated by the artifacts in the upper part of this picture, the approach is not perfect yet. Eventually I will have to improve this.

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Snails III

While the outside of the snails presented so far looks more or less satisfactory, the inside does not. There are problems in particular, when individual turns of the snail are overlapping (as they often are). Here is a first, rough solution to this problem using subsequent (partial) circular arches to construct snails with overlapping turns.

Snail shell

Snail shell

Unfortunately it turned out to be quite difficult to get such constructions any smoother, so I turned to a more thorough approach, constructing snails from small disks (arranged in the right way) combined to a blob. To demonstrate this approach first the individual disks are given.

Concept shell

Concept shell

The produce a solid snail, these disks are enlarged and combined into a blob.

Blob shell

Blob shell

Using two layers of such disks (an internal and an external), it is possible to produce a snail with different textures on the inside and the outside.

Two-coloured shell

Two-coloured shell

Within certain limits it is possible to change the geometry of such snails.

Flat snail

Flat snail

Here comes the limit to this approach. Changing the geometry of the turns themselves leads to problems. Still the structures look nice, but certainly not state of the art… (To be continued…)

Elongated snail

Elongated snail

Elongated snail

Elongated snail
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Snails II

Almost any object can be used for rotating on the path of a logarithmic spiral. I start this example with a cube in two orientations. First with each cube separated by 10 degrees.

Cubic snail

Cubic snail

Cubic snail

Cubic snail

When each cube is separated by only 1 degree, the resulting structures appear pretty smooth.

Cubic snail

Cubic snail

Cubic snail

Cubic snail

While these structures do not look very natural, here are some more natural shells formed from distorted spheres.

Shell 1

Shell 1

Shell 2

Shell 2

When using blobs for constructing such structures, it is possible to decorate the outside with various details:

Shell 3

Shell 3
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Pandemic

It is a somewhat alarmist issue, but nevertheless, here are some visual contributions covering the global spread of viral diseases.

Pandemic

Pandemic

Pandemic

Pandemic

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Snails I

Shells from snails often can be derived from a logarithmic spiral, which is given here. In such a spiral the radius is increasing exponentially with increasing revolutions.

Logarithmic spiral

Logarithmic spiral

In this case, in addition to the exponentially increasing radius, the spiral is increasing exponentially in a direction perpendicular to its revolutions.

Logarithmic spiral

Logarithmic spiral

Nice snails can be constructed by increasing the thickness of the red helix (again in an exponential way).

Simple snail

Simple snail

By subtracting a slightly smaller structure, the shells become hollow.

Open snail

Open snail

Sectioned snail

Sectioned snail

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Cellular structures II

My first posting on cellular structures represented a normal parenchymatic tissue. In addition, here are some more specialized tissues:

Using random positions (golden spheres) and connecting adjacent positions it is possible to generate a cellular structure, …

… which resembles an aerenchyma.

Aerenchyma

Aerenchyma

Here comes a section from such a tissue.

Aerenchyma, section

Aerenchyma, section

And using random positions …

Random positions

Random positions

… and subtracting them from a solid block it is possible to obtain sponge-like structures.

Sponge formation

Sponge formation
Sponge structure

Sponge structure

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Filamentous cyanobacteria

Similar as described for Microcystis in the previous posting from this category, most organisms introduced in this posting are able to form large algal blooms. Such blooms are deleterious to other organisms (in particular to vertebrates), because degradation of the accumulating algal mats uses up much oxygen resulting in suffocating conditions and because many of such cyanobacteria are producing effective and stable toxins. The only organism not involved in such blooms is Spirulina, which, in contrast, is rather used as a dietary supplement for human (and animal) nutrition. Although this practice is very old, it is still difficult to prove or disprove the effectiveness of such supplements.

Anabaena presents the most simple form of cyanobacterial filament formation. Roundish cells similar to those from non-filamentous cyanobacteria are attached to each other in the form of a filament. From time to time heterocysts (of slightly larger size) necessary for nitrogen fixation are included in such filaments. In addition to its involvement in algal blooms, one species (Anabaena azollae) can form a symbiosis with the water fern Azolla.

Anabaena

Anabaena

Anabaena

Anabaena

In the case of Aphanizomenon, normal cells and heterocysts are more adapted to filament formation…

Aphanozimenon

Aphanozimenon

… and this adaptation goes even further in the case of Lyngbya, with its flat cylindrical cells.

Lyngbya

Lyngbya

Lyngbya

Lyngbya

Spirulina is formed in a similar way as Lyngbya from small cylindrical cell. In microscopic images from this cyanobacterium, these cells are hard to see. So I chose a presentation showing only the outer form of this interesting bacterium.

Spirulina

Spirulina

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Virtual Globe

A globe constructed exclusively from 0 and 1; Here comes my contribution to topics like virtual reality, global modeling etc.

Virtual Globe

Virtual Globe

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Non-filamentous cyanobacteria II

This second post on non-filamentous cyanobacteria is about different forms of colony formation, which depend on the geometry of cell division. Aphanotheca, which has been shown in an earlier posting on cyanobacteria is a simple example, where the plains of cell division are oriented randomly and the new cells are surrounded by a common spherical matrix. Aphanotheca is a large genus with many species distributed in a wide range of habitats.

Aphanotheca

Aphanotheca

Genera like Microcystis divide in a random way as well, but the resulting cells are integrated in irregular rather than spherical structures. Members of this genus are able to accumulate in large numbers under suitable conditions forming large algal blooms. Such blooms often result in oxygen deprivation of the waters affected and eventually are responsible for the production of specific toxins.

Microcystis

Microcystis

On the other hand, there are cyanobacteria dividing in a very regular way, like, in this example, Chroococcus. The colonies of Chroococcus are formed by two subsequent divisions, with the plain of division turned by 90 degress.

Chroococcus

Chroococcus

Chroococcus

Chroococcus

Colonies of Merismopedia are formed by a very similar principle. Plains of subsequent divisions are turned by 90 degrees. In addition this rotation of the plain of division always occurs around the same axis. Here colonies are separated from each other only after a considerable amount of divisions. This way Merismopedia is able to form extended sheets.

Merismopedia

Merismopedia

Merismopedia

Merismopedia
Merismopedia

Merismopedia

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Cells and soap bubbles

Coming back to a recent posting about modeling cellular structures, I learnt from a book by Philip Ball (Shapes, Nature’s Patterns: a tapestry in three parts, Oxford University Press from 2007) that soap bubbles can serve as a simple models of cells. (This book will be cited several times in future postings…). So I started to draw simple groups of soap bubbles by using blobs in a similar way as figured out in the posting on cellular structures.

Two bubbles

Two bubbles

Smaller bubbles have higher internal pressures, so they will expand into larger bubbles.

Two uneven bubbles

Two uneven bubbles

Here comes a group of three bubbles …

Three bubbles

Three bubbles

…and here a group of 4. (Does it start to look somehow familiar to cells?)

Four bubbles

Four bubbles

When we imagine a layer of such uniform bubbles, we will end up with a classical honeycomb…

Honeycomb

Honeycomb

…which again resembles the shape of some cellular arrangements.

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