- To push the boundaries of code/computation.
- Examine the fundamental idea of an algorithm.
- Has been done before with information, cf. Shannon.
- Test computability, are non-computable ideas unphysical?
- Central Irrelevant Topics Paradigm: Divide by zero.

A infinite "tape" of finite symbols.

A "head" with an internal state that

can advance only one spot at a time.

A finite set of instructions:

given a state and symbol perform set action.

- Embody the idea of Turing's original tape machine.
- (very) Limited set of instructions.
- (very) Limited set of symbols.
- Create obfuscated, impossible to maintain codes.
- Extremely simple compilers.
- Serves as a model to construct higher-order languages.

- Extension of one-dimensional Turing tape machine.
- Live in metric spaces with coordinate systems.
- Usually Cartesian, but not necessarily.
- Considered a "funge" if topology is toroidal.
- More exotic topologies are classified as fungeoids.

- Extreme minimalism: Turing tarpit
- Designed to challenge and amuse programmers
- Not suitable for practical use
- Smallest compiler only 200 bytes!

**>**increment the data pointer**<**decrement the data pointer**+**increment the byte at the data pointer**-**decrement the byte at the data pointer**.**output the value of the byte at the data pointer**[**if the byte at the data pointer is zero, then instead of moving the instruction pointer forward to the next command, jump it forward to the command after the matching ] command.**]**if the byte at the data pointer is nonzero, then instead of moving the instruction pointer forward to the next command, jump it back to the command after the matching [ command.**,**accept one byte of input, storing its value in the byte at the data pointer.

Hello World

```
++++++++++[>+++++++>++++++++++>+++>+<<<<
-]>++.>+.+++++++..+++.>++.<<+++++++++++++++
.>.+++.------.--------.>+.>.
```

The first line initializes a[0] = 10 by simply incrementing ten times from 0. The loop from line 2 effectively sets the initial values for the array: a[1] = 70 (close to 72, the ASCII code for the character 'H'), a[2] = 100 (close to 101 or 'e'), a[3] = 30 (close to 32, the code for space) and a[4] = 10 (newline). The loop works by multiplying the value of a[0], 10, by 7, 10, 3, and 1, saving the results in other cells. After the loop is finished, a[0] is zero. >++. then moves the pointer to a[1] which holds 70, adds two to it (producing 72 which is the ASCII character code of a capital H), and outputs it.

- Stack-based, Turing-tape style language.
- Programs are arranged on a two-dimensional grid.
- Tape has the topology of a toroid.
- Arrow instructions direct the control flow.
- Loops are constructed by sending the control flow in a cycle.
- Befunge is a proper funge, and higher dimensional funges exist such as Trefunge.

Hello World

```
vv < <
2
^ v<
v13v4
^ ^
> >?> ?>5^
v v
v97v6
v v<
8
. > > ^
^<
```

- Ignores all characters but whitespace.
- Each whitespace combination forms a bit-pattern.
- Whitespace can be a polyglot.
- Stenographic capabilities.
- Challenges the idea of symbol and tape instructions.
- Proof of Turning completeness is now CS homework.

Hello World

` Say Hello`

Given the state of the program: the next action is taken

according to a probability distribution

Getting even trivial programs to have a reliable output is often a monumental task. Useful for exploring large search spaces, quantum computing, machine learning, ...

- Unreliable (a feature not a bug!)
- What is the notion of computability for a ND machine?
- Expectation values of computability, Turing is a special case
- Is Godel's incompleteness theorem even valid?

How many ideas of physics can be

expressed under the C&L topology?

Chutes and Ladders Potential Function?

C&L does not possess a typical energy landscape; rather it is a stochastically driven process with discrete jumps.

time-invariance. represents the probability from

state , and .

Single player Game Length Attention Span

, , , , ,

Exponential Maps, and flows give rise to a differential-mapping. A set of coupled first-order differential equations has a natural connection to Markov chains:

The Markov matrix is the *generator* of the rate matrix at a given time:

Assume that the die rolls now represent rates (like a chemical equation), i.e. the first roll would be:

This system of equations can be exponential to give a continuous-time Markov game.

['height:300px']

,

Note the abissica on the second picture,

we are modeling fractions of a die roll!