I am trying to design a novel number system to design a novel number-system based game.

To do this, I want to create a mapping from a set S of symbols to the integers, where, not all sequences of symbols from S are allowed, but, they can all map according to one rule, onto the natural numbers.

I want to start with one such number system and see if the user can carry out addition and multiplication in the game using the game number system mechanics (this, would be the scope, and, the fun, of the game).

However, in order to do this I would have to start with one specific set of symbols and mapping, (and, start playing, before development, to see how the rules go).

I wonder whether anyone can come up with such an implementation.

This, is something, that, can be managed, as a game, on a mobile phone (but may require some writing to figure the rules out, (e.g., what would make a good set of rules for a game)).

So, while there are many instances, I am looking (for, some perhaps optimal), suggestions.

One could map the symbols, carry out the operations in the space of the usually represented natural numbers, and then take the inverse (to, retrieve... the original symbol), but in the game one would have to carry out everything in the original number system representation (and the rules, would, have to be given in the interface).

Thanks.

EDIT: A 3D visualization approach might be to place all cross product of symbols, sequences of length 1 of symbols followed by all sequences of length 2 followed by all sequences of length 3, on the z-axis with sequences growing on the x-axis, and an x on the z-axis to indicate that the sequence is allowed, and an arrow to the Arabic numeral number on the y-axis the sequence on the zx-plane maps to.

Thanks.

I am trying to design a novel number system for a game.

To do this, I want to create a mapping from a set S of symbols to the integers, where not all sequences of symbols from S are allowed, but they can all map onto the natural numbers according to one rule.

I want to start with one such number system and see if the user can carry out addition and multiplication in the game using the game number system mechanics (this would be the scope and the fun of the game).

However, in order to do this, I would have to start with one specific set of symbols and mapping and start playing, before development, to see how the rules go.

I wonder whether anyone can come up with such an implementation.

This is, something that can be managed as a game on a mobile phone, but may require some writing to figure the rules out.

So, while there are many instances, I am looking for some (perhaps optimal) suggestions.

One could map the symbols, carry out the operations in the space of the usually represented natural numbers, and then take the inverse (to retrieve the original symbol), but in the game one would have to carry out everything in the original number system representation (and the rules would have to be given in the interface).

A 3D visualization approach might be to place all cross products of symbols, sequences of length 1 of symbols followed by all sequences of length 2 followed by all sequences of length 3, on the z-axis, with sequences growing on the x-axis, and an x on the z-axis to indicate that the sequence is allowed, and an arrow to the Arabic numeral number on the y-axis the sequence on the zx-plane maps to.

I am trying to design a novel number system to design a novel number-system based game.

To do this, I want to create a mapping from a set S of symbols to the integers, where, not all sequences of symbols from S are allowed, but, they can all map according to one rule, onto the natural numbers.

I want to start with one such number system and see if the user can carry out addition and multiplication in the game using the game number system mechanics (this, would be the scope, and, the fun, of the game).

However, in order to do this I would have to start with one specific set of symbols and mapping, (and, start playing, before development, to see how the rules go).

I wonder whether anyone can come up with such an implementation.

This, is something, that, can be managed, as a game, on a mobile phone (but may require some writing to figure the rules out, (e.g., what would make a good set of rules for a game)).

So, while there are many instances, I am looking (for, some perhaps optimal), suggestions.

One could map the symbols, carry out the operations in the space of the usually represented natural numbers, and then take the inverse (to, retrieve... the original symbol), but in the game one would have to carry out everything in the original number system representation (and the rules, would, have to be given in the interface).

Thanks.

I am trying to design a novel number system to design a novel number-system based game.

To do this, I want to create a mapping from a set S of symbols to the integers, where, not all sequences of symbols from S are allowed, but, they can all map according to one rule, onto the natural numbers.

I want to start with one such number system and see if the user can carry out addition and multiplication in the game using the game number system mechanics (this, would be the scope, and, the fun, of the game).

However, in order to do this I would have to start with one specific set of symbols and mapping, (and, start playing, before development, to see how the rules go).

I wonder whether anyone can come up with such an implementation.

This, is something, that, can be managed, as a game, on a mobile phone (but may require some writing to figure the rules out, (e.g., what would make a good set of rules for a game)).

So, while there are many instances, I am looking (for, some perhaps optimal), suggestions.

One could map the symbols, carry out the operations in the space of the usually represented natural numbers, and then take the inverse (to, retrieve... the original symbol), but in the game one would have to carry out everything in the original number system representation (and the rules, would, have to be given in the interface).

Thanks.

EDIT: A 3D visualization approach might be to place all cross product of symbols, sequences of length 1 of symbols followed by all sequences of length 2 followed by all sequences of length 3, on the z-axis with sequences growing on the x-axis, and an x on the z-axis to indicate that the sequence is allowed, and an arrow to the Arabic numeral number on the y-axis the sequence on the zx-plane maps to.

Thanks.

I am trying to design a novel number system to design a novel number-system based game.

To do this, I want to create a mapping from a set S of symbols to the integers, where, not all sequences of symbols from S are allowed, but, they can all map according to one rule, onto the natural numbers.

I want to start with one such number system and see if the user can carry out addition and multiplication in the game using the game number system mechanics (this, would be the scope, and, the fun, of the game).

However, in order to do this I would have to start with one specific set of symbols and mapping, (and, start playing, before development, to see how the rules go).

I wonder whether anyone can come up with such an implementation.

This, is something, that, can be managed, as a game, on a mobile phone (but may require some writing to figure the rules out, (e.g., what would make a good set of rules for a game)).

So, while there are many instances, I am looking (for, some perhaps optimal), suggestions.

Thanks.

I am trying to design a novel number system to design a novel number-system based game.

To do this, I want to create a mapping from a set S of symbols to the integers, where, not all sequences of symbols from S are allowed, but, they can all map according to one rule, onto the natural numbers.

I want to start with one such number system and see if the user can carry out addition and multiplication in the game using the game number system mechanics (this, would be the scope, and, the fun, of the game).

However, in order to do this I would have to start with one specific set of symbols and mapping, (and, start playing, before development, to see how the rules go).

I wonder whether anyone can come up with such an implementation.

This, is something, that, can be managed, as a game, on a mobile phone (but may require some writing to figure the rules out, (e.g., what would make a good set of rules for a game)).

So, while there are many instances, I am looking (for, some perhaps optimal), suggestions.

One could map the symbols, carry out the operations in the space of the usually represented natural numbers, and then take the inverse (to, retrieve... the original symbol), but in the game one would have to carry out everything in the original number system representation (and the rules, would, have to be given in the interface).

Thanks.