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{{about|the programming language|the vaccine development tool|MIMIC (Immunology)|other uses|Mimic (disambiguation)}}

'''MIMIC''', known in capitalized form only, is a former [[simulation]] [[computer language]] developed 1964 by [[H. E. Petersen]], F. J. Sansom and L. M. Warshawsky of Systems Engineering Group within the [[Air Force Materiel Command]] at the [[Wright-Patterson AFB]] in [[Dayton, Ohio]], United States.<ref>[http://stinet.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=AD0656301 Defense Technical Information Center]{{dead link|date=June 2022|bot=medic}}{{cbignore|bot=medic}}</ref> It is an [[expression-oriented programming languages|expression-oriented]] continuous block simulation language, but capable of incorporating blocks of [[FORTRAN]]-like algebra.

MIMIC is a further development from MIDAS ('''M'''odified '''I'''ntegration '''D'''igital '''A'''nalog '''S'''imulator), which represented [[analog computer]] design. Written completely in FORTRAN but one routine in [[COMPASS]], and ran on [[Control Data Corporation|Control Data]] [[supercomputer]]s, MIMIC is capable of solving much larger simulation models.

With MIMIC, [[ordinary differential equation]]s describing [[mathematical model]]s in several scientific disciplines as in engineering, physics, chemistry, biology, economics and as well as in social sciences can easily be solved by [[numerical integration]] and the results of the analysis are listed or drawn in diagrams. It also enables the analysis of [[nonlinearity|nonlinear dynamic condition]]s.

The MIMIC software package, written as FORTRAN overlay programs, executes input statements of the mathematical model in six consecutive passes. Simulation programs written in MIMIC are compiled rather than interpreted. The core of the simulation package is a variable step numerical integrator of fourth-order [[Runge-Kutta method]]. Many useful functions related to electrical circuit elements exist besides some mathematical functions found in most scientific programming languages. There is no need to sort the statements in order of dependencies of the variables, since MIMIC does it internally.

Parts of the software organized in overlays are:
*MIMIN (input)– reads in user simulation program and data,
*MIMCO (compiler) – compiles the user program and creates an in-core array of instructions,
*MIMSO (sort)– sorts the instructions array after dependencies of variables,
*MIMAS (assembler) – converts the [[Binary-coded decimal|BCD]] instructions into [[machine code|machine-oriented code]],
*MIMEX (execute)– executes the user program by integrating,
*MIMOUT (output)– puts out the data as a list or diagram of data.

==Example==
;Problem:
Consider a predator-prey model from the field of [[marine biology]] to determine the dynamics of fish and shark populations. As a simple model, we choose the [[Lotka–Volterra equation]] and the constants given in a tutorial.<ref>{{cite web |url=http://fluid.stanford.edu/~fringer/teaching/numerical_methods_02/tutorials/tutorial2.pdf |publisher=Stanford University-Dept of Civil and Environmental Engineering, Environmental Fluid Mechanics Lab |title=Tutorial 2: Numerical Solutions of ODE's |date=2002-08-19 |accessdate=2012-02-26 |url-status=dead |archiveurl=https://web.archive.org/web/20100720073318/http://fluid.stanford.edu/~fringer/teaching/numerical_methods_02/tutorials/tutorial2.pdf |archivedate=2010-07-20 }}</ref>

If
: ''f''(t): Fish population over time (fish)
: ''s''(t): Shark population over time (sharks)
: d''f'' / dt or <math>\dot f</math>: growth rate of fish population (fish/year)
: d''s'' / dt or <math>\dot s</math>: growth rate of shark population (sharks/year)
: <math>\alpha</math>: growth rate of fish in the absence of sharks (1/year)
: <math>\beta</math>:  death rate per encounter of fish with sharks (1/sharks and year).
: <math>\gamma</math>: death rate of sharks in the absence of their prey, fish (1/year)
: <math>\epsilon</math>: efficiency of turning predated fish into sharks (sharks/fish)
then
: <math> \dot f = \alpha f - \beta f s </math> 
: <math> \dot s = \epsilon \beta f s - \gamma s </math>
with initial conditions
: <math> f(0) = f_o </math>
: <math> s(0) = s_o </math>

The problem's constants are given as:
*<math>f_o</math> = 600 fish
*<math>s_o</math> = 50 sharks
*<math>\alpha</math> = 0.7 fish/year
*<math>\beta</math> = 0.007 fish/shark and year
*<math>\gamma</math> = 0.5 shark/year
*<math>\epsilon</math> = 0.1 shark/fish
*tmax = 50 year

;Code sample:

 Card columns
 0        1         2         3         4         5         6         7
 12345678901234567890123456789012345678901234567890123456789012345678901
 -----------------------------------------------------------------------
 * A SIMPLE PREDATOR-PREY MODEL FROM MARINE BIOLOGY
 / (TUTORIAL 2: NUMERICAL SOLUTION OF ODE'S - 19/08/02)
 / ENVIRONMENTAL FLUID MECHANICS LAB
 / DEPT OF CIVIL AND ENVIRONMENTAL ENGINEERİNG
 / STANFORD UNIVERSITY
 *
 * LOTKA–VOLTERRA EQUATION
                   CON(F0,S0,TMAX)
                   CON(ALPHA,BETA,GAMMA,EPS)
           1DF   = ALPHA*F-BETA*F*S
           F     = INT(1DF,F0)
           1DS   = EPS*BETA*F*S-GAMMA*S
           S     = INT(1DS,S0)
                   HDR(TIME,FISH,SHARK)
                   OUT(T,F,S)
                   PLO(F,S)
                   FIN(T,TMAX)
                   END
 <EOR>
 600.       50.          50.
 0.7        0.007        0.5         0.1
 <EOF>

==References==
{{reflist}}
;Notes
{{refbegin}}
* Control Data MIMIC; A Digital Simulation Language, Reference Manual, Publication Number 4461n400, Control Data Corporation, Special Systems Publications, St. Paul, Minnesota (April 1968)
* MIMIC, An Alternative Programming Language for Industrial Dynamics, N.D. Peterson, Socio-Econ Plan Sci. 6, Pergamon 1972
*[http://bitsavers.vt100.net/pdf/oregonState/os3/CC-69-05_MIMIC_Apr69.pdf MIMIC Manual (1969), Computer Center Oregon State University]{{dead link|date=May 2017 |bot=InternetArchiveBot |fix-attempted=yes }}
{{refend}}

{{Control Data Corporation}}

[[Category:Object-oriented programming languages]]
[[Category:Numerical programming languages]]
[[Category:Simulation programming languages]]
[[Category:Control Data Corporation software]]
[[Category:Wright-Patterson Air Force Base]]
[[Category:Programming languages created in 1964]]
[[Category:Fortran software]]