Physarum polycephalum is one more protist which doesn't fit kingdoms of plantae, animals and fungi. Neither bacteria. So it is already interesting. Another interesting thing is that our chair is involved in the European project Phychip, which is focusing on physarum polycephalum and unconventional computing.

## Physarum Polycephalum and its life cycle

"Physarum polycephalum, literally the "many-headed slime", is a slime mold that inhabits shady, cool, moist areas, such as decaying leaves and logs. Like slime molds in general, it is sensitive to light; in particular, light can repel the slime mold and be a factor in triggering spore growth."(wikipedia A) It feeds on bacteria, spores and other microbial creatures.

- Vegetative phase: plasmodium (consists of networks of protoplasmic veins, and many nuclei)
- sclerotium (hardened multinucleated tissue)
- sporangia

- "Physarum Polycephalum exhibit a form of intelligence
- When separated they will pull themselves back together
- They also exhibit self-sacrifice
- They will gather and form a stalk and then a fruiting body
- Those self making up the stalk will die. Those at the top will clump into a ball made of life spores" (Bonner)

https://www.youtube.com/watch?v=bkVhLJLG7ug&list=PLb14u5e_rEcSVd0ZjgEFHuggA6y7ozQQI

## Physarum Experiments

HOWTO @ Adamatzky (2010). Chapter 2

## Physarum Machine

"Unconventional computing is an interdisciplinary of science where computer scientists, physicists, mathematicians, apply principles of information processing in natural systems to design novel computer devices and architectures" (Adamatzky 2007)

“The plasmodium functions as a parallel amorphous computer with parallel inputs and parallel outputs. Data are represented by spatial configurations of sources of nutrients. A program of computation is coded via configurations of repellents and attractants. Results of computation are presented by the configuration of the protoplasmic network and the localisation of the plasmodium.”(Adamatzky 2010)

“.. plasmodium is unique biological substrate that mimics universal storage modification machines, namely the Kolmogorov-Uspensky machine. In the plasmodium implementation of the storage modification machine data are represented by sources of nutrients and memory structure by protoplasmic tubes connecting the sources. In laboratory experiments and simulation we demonstrate how the plasmodium-based storage modification machine can be programmed.”(Adamatzky & Jones 2009)

Implementations

- Implementation of a Kolmogorov–Uspensky machine on a biological substrate. (Adamatzky 2007)
- Programmable reconfiguration of Physarum machines (Adamatzky 2009)

### Computable Discrete Elements in the Turing Machine

In a 1936 paper by Turing, the concept of the machine is proposed as the simple idea of an apparatus which is able to compute discrete values – zeros and ones. In the same paper, Turing introduces a computing machine with an infinite length of tape and a tape head acting upon seven commands: a) read the tape, b) move the tape left, c) move tape right, d) write “zero” on the tape, e) write “one” on the tape, f) jump to another command, and g) halt. The idea of these commands is to show that output B could be processed having an initial state and some input A. The position of the tape head on the proposed apparatus processing the information is dependent on the information stored on the tape: If the input information is defined, so is the output. The problem in such a computational model is any numerically undefined variable which would cause the machine to stop processing information, or to "halt." The halting state or, according to Turing, the “decision problem" (Enscheidungsproblem) is the problem of digital computation being defined by numerical variables. Thus, the Turing machine is limited to computing all input information and to solving all given problems (Turing 1936).

Turing Machines: https://www.youtube.com/watch?v=gJQTFhkhwPA

### Markov chain

"A Markov chain (discrete-time Markov chain or DTMC[1]), named after Andrey Markov, is a random process that undergoes transitions from one state to another on a state space. It must possess a property that is usually characterized as "memorylessness": the probability distribution of the next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of "memorylessness" is called the Markov property. Markov chains have many applications as statistical models of real-world processes."(wikipedia (b))

### Kolmogorov Machine

"Kolmogorov, or Kolmogorov-Uspensky, machines [Ko1, KU, US] are similar to Turing machines except that the tape can change its topology."(Gurevich) Also, as far as I understand, Kolmogorov Machine isn't described by discrete 0 and 1 values. Also its functions could be updated in real time over the recursive method. On the other hand both Turing Machine and Kolmogorov machine, could emulate each other, so at the end the difference is just in the way how the machines compute their functions.

"Мы остановимся на следующих вариантах математического опреде ления вычислимой функции или алгоритма: A) Определение вычислимой функции как функции, значения которой выводимы в некотором логическом исчислении (Гёдель [4], Чёрч [5]1)). Б) Определение вычислимой функции как функции, значения кото рой получаются при помощи исчисления Х-коиверсии Чёрча [5], [7]. B) Определение вычислимой функции как функции частично-рекур сивной (см. работу Клини [8])2) или —для случая всюду определенной функции —как общерекурсивной (Клини [10]). (Термины «частично-рекур сивная» и «общерекурсивная» понимаются здесь в смысле приложения I). Г) Вычислительная машина Тьюринга [ И ] 3 ) . Д) Финитный комбинаторный процесс Поста [13]. Е) Нормальный алгорифм А. А. Маркова [1], [2]." (Колмогоров & Успенский 1958)

"Kolmogorov machines tape similarly to Schönhage’s tape is a finite connected graph with a distinguished (active) node. They work upon partly recursive function, changing instructions in real time." (Gurevich)

"Instructions: 1. add a new node together with a pair of edges of some colors between the active node and the new one, 2. remove a node and the edges incident to it, 3. add a pair of edges of some colors between two existing nodes, 4. remove the two edges between two existing nodes, 5. halt. "(Gurevich)

"Grigoriev [Gr] exhibited a function real-time computable by some KU machine but not real-time computable by any Turing machine."(Gurevich)

## Projects

1. Sonification. James Whitting, Ben De Lacy Costello, Andrew Adamatzky Towards slime mould chemical sensor: Mapping chemical inputs onto electrical potential dynamics of Physarum Polycephalum Sensors and Actuators B: Chemical. response to BenzylAlcohol https://www.youtube.com/watch?v=byTJEYHaIIM https://soundcloud.com/lessnullvoid/physarum-sonification

2. Leslie Garcia and Paloma López. Machine shop. "Video made during the workshop Bio Machines cultural center in the 77 organized by the Laboratory of Digital Citizenship. Participants cultured Physarum polycephalum samples to understand their life cycle. They also modified web cameras to turn them into microscopes inexpensive (28 pesos each) and to closely observe their growth and oscillations using software written with processing." https://www.youtube.com/watch?v=4sp9Efokv4o

3. Toshiyuki Nakagaki. 3-5 min https://www.youtube.com/watch?v=2UxGrde1NDA

## References

- Andrew Adamatzky (2007). Adamatzky A. Physarum machine: implementation of a Kolmogorov–Uspensky machine on a biological substrate. Available at: http://arxiv.org/pdf/cs/0703128.pdf (Accessed 8 December 2015).
- Andrew Adamatzky and Jeff Jones (2009). Programmable reconfiguration of Physarum machines. Available at: http://arxiv.org/pdf/0901.4556.pdf (Accessed 8 December 2015).
- Andrew Adamatzky (2010). Physarum Machines: Computers from Slime Mould. World Scientific Publishing. Partly available at: https://books.google.de/books?id=Kbs_AIDbfU8C&printsec=frontcover (Accessed 8 December 2015).
- John Bonner. Available at: https://www.youtube.com/watch?v=bkVhLJLG7ug&list=PLb14u5e_rEcSVd0ZjgEFHuggA6y7ozQQI (Accessed 8 December 2015).
- Yuri Gurevich (1988). On Kolmogorov Machines And Related Issues. Available at: http://research.microsoft.com/en-us/um/people/gurevich/opera/78.pdf (Accessed 8 December 2015).
- А. Н. Колмогоров и В. А. Успенский (1958). “К ОПРЕДЕЛЕНИЮ АЛГОРИТМА”, УСПЕХИ МАТЕМАТИЧЕСКИХ НАУК, т. XIII, вып. 4 (82). Available at http://lpcs.math.msu.su/~uspensky/bib/Uspensky_1958_UMN_Kolmogorov_Opredelenie_algoritma.pdf (Accessed 8 December 2015).
- Emil Post (1036). Finite Combinatory Processes-Formulation 1. Available at: https://www.wolframscience.com/prizes/tm23/images/Post.pdf (Accessed 8 December 2015).
- Turing, A. M. (1936). “On computable numbers, with an application to the Entscheidungsproblem,” in Proceedings of the London mathematical society, 2(42), pp. 230-265. Available at: http://www.dna.caltech.edu/courses/cs129/caltech_restricted/Turing_1936_IBID.pdf (Accessed 8 December 2015).
- wikipedia (a). Physarum polycephalum. Available at: https://en.wikipedia.org/wiki/Physarum_polycephalum (Accessed 8 December 2015).
- wikipedia (b). Markov chain. Available at: https://en.wikipedia.org/wiki/Markov_chain (Accessed 8 December 2015).
- wikipedia (c). Random-access machine. Available at: https://en.wikipedia.org/wiki/Random-access_machine (Accessed 8 December 2015).