Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 TupperDecipher

Source Notebook

Decrypt with Tupper’s self-referential formula

Contributed by: Aster Ctor

ResourceFunction["TupperDecipher"][secret,p]

decrypts integer secret using prime key p.

Details and Options

Tupper’s self-referential formula is a formula that visually represents itself when graphed at a specific location in the xy-plane.
The formula was defined by Jeff Tupper and appears as an example in Tupper's 2001 SIGGRAPH paper on reliable two-dimensional computer graphing algorithms.
ResourceFunction["TupperDecipher"] decodes an integer k into an image according to this principle.
The following options can be used to control the output style:
The option "Column" can be used to control the number of columns in the output.

Examples

Basic Examples (2) 

Decrypt Tupper’s self-referential formula:

In[1]:=
ResourceFunction[ "TupperDecipher"][4858450636189713423582095962494202044581400587983244549483093085061934704708809928450644769865524364849997247024915119110411605739177407856919754326571855442057210445735883681829823754139634338225199452191651284348332905131193199953502413758765239264874613394906870130562295813219481113685339535565290850023875092856892694555974281546386510730049106723058933586052544096664351265349363643957125565695936815184334857605266940161251266951421550539554519153785457525756590740540157929001765967965480064427829131488548259914721248506352686630476300, 17]
Out[1]=

Decrypt some other pattern:

In[2]:=
ResourceFunction["TupperDecipher"][179057560799192115125, 5]
Out[2]=

Options (1) 

"Column" is a positive integer used to control the number of columns in the output:

In[3]:=
ResourceFunction["TupperDecipher"][179057560799192115125, 5, "Column" -> 3]
Out[3]=

Possible Issues (4) 

Here is a secret:

In[4]:=
secret = 945891878351701858524088616446793108690613698185274018507104850541719233640398556238111269691108214787733417842585442401364834976;

The correct key gives recognizable results:

In[5]:=
ResourceFunction["TupperDecipher"][secret, 11]
Out[5]=

Some keys cannot be used to decode secret, in which case a message is issued:

In[6]:=
ResourceFunction["TupperDecipher"][secret, 7]

Sometimes secret can be unlocked but it is unrecognizable:

In[7]:=
ResourceFunction["TupperDecipher"][secret, 13]
Out[7]=

Publisher

Aster Ctor (MoeNet)

Version History

  • 2.0.0 – 30 December 2019
  • 1.0.0 – 26 December 2019

Source Metadata

  • Citation:
    • Tupper, J., "Reliable two-dimensional graphing methods for mathematical formulae with two free variables." In: SIGGRAPH '01: Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, 77–86. New York: Association for Computing Machinery, 2001. DOI: 10.1145/383259.383267

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