Rippling Images

Make animated GIFs that simulate the effect of a reflection distorted in water.

Use natural language to request a picture of something:

Hint: try a common type of animal, or a famous person.

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There are lots of ways to get pictures in the Wolfram Language.

On the desktop, you can take a picture with your computers camera using CurrentImage.

You can use the Wolfram Knowledgebase (the same one that powers Wolfram|Alpha) to ask for a picture of something. Hold down the key and press = to get a natural language input field ():

\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "picture of an elephant", WolframAlphaClient`Private`boxes$$ = RowBox[{"EntityValue", "[", RowBox[{ TemplateBox[{"\"elephants\"", RowBox[{"Entity", "[", RowBox[{"\"Species\"", ",", "\"Family:Elephantidae\""}], "]"}], "\"Entity[\\\"Species\\\", \\\"Family:Elephantidae\\\"]\"", "\"species specification\""}, "Entity"], ",", TemplateBox[{"\"image\"", RowBox[{"EntityProperty", "[", RowBox[{"\"Species\"", ",", "\"Image\""}], "]"}], "\"EntityProperty[\\\"Species\\\", \\\"Image\\\"]\""}, "EntityProperty"]}], "]"}], WolframAlphaClient`Private`allassumptions$$ = {{ "type" -> "MultiClash", "word" -> "", "template" -> "Assuming ${word1} is referring to ${desc1}. Use \ \"${word2}\" as ${desc2}. Use \"${word3}\" as ${desc3}. Use \ \"${word4}\" as ${desc4}.", "count" -> "4", "Values" -> {{ "name" -> "Species", "word" -> "elephant", "desc" -> "a species specification", "input" -> "*MC.%7E-_*Species-"}, { "name" -> "Periodical", "word" -> "elephant", "desc" -> "a periodical", "input" -> "*MC.%7E-_*Periodical-"}, { "name" -> "Movie", "word" -> "elephant", "desc" -> "a movie", "input" -> "*MC.%7E-_*Movie-"}, { "name" -> "WordData", "word" -> "", "desc" -> " referring to English words", "input" -> "*MC.%7E-_*WordData-"}}}, { "type" -> "SubCategory", "word" -> "elephant", "template" -> "Assuming ${desc1}. Use ${desc2} instead", "count" -> "2", "Values" -> {{ "name" -> "Family:Elephantidae", "desc" -> "elephants", "input" -> "*DPClash.SpeciesE.elephant-_*Family%\ 3AElephantidae-"}, { "name" -> "Species:LoxodontaAfricana", "desc" -> "Loxodonta africana", "input" -> "*DPClash.SpeciesE.elephant-_*Species%\ 3ALoxodontaAfricana-"}}}}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{135., {7., 16.}}, TrackedSymbols:>{ WolframAlphaClient`Private`query$$, WolframAlphaClient`Private`boxes$$, WolframAlphaClient`Private`allassumptions$$, WolframAlphaClient`Private`assumptions$$, WolframAlphaClient`Private`open$$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{WolframAlphaClient`Private`open$$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)

You can also drag images from most websites and drop them directly into the code. If you want to refer to it later you can always give it a name like image:

image = \!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "picture of an elephant", WolframAlphaClient`Private`boxes$$ = RowBox[{"EntityValue", "[", RowBox[{ TemplateBox[{"\"elephants\"", RowBox[{"Entity", "[", RowBox[{"\"Species\"", ",", "\"Family:Elephantidae\""}], "]"}], "\"Entity[\\\"Species\\\", \\\"Family:Elephantidae\\\"]\"", "\"species specification\""}, "Entity"], ",", TemplateBox[{"\"image\"", RowBox[{"EntityProperty", "[", RowBox[{"\"Species\"", ",", "\"Image\""}], "]"}], "\"EntityProperty[\\\"Species\\\", \\\"Image\\\"]\""}, "EntityProperty"]}], "]"}], WolframAlphaClient`Private`allassumptions$$ = {{ "type" -> "MultiClash", "word" -> "", "template" -> "Assuming ${word1} is referring to ${desc1}. Use \ \"${word2}\" as ${desc2}. Use \"${word3}\" as ${desc3}. Use \ \"${word4}\" as ${desc4}.", "count" -> "4", "Values" -> {{ "name" -> "Species", "word" -> "elephant", "desc" -> "a species specification", "input" -> "*MC.%7E-_*Species-"}, { "name" -> "Periodical", "word" -> "elephant", "desc" -> "a periodical", "input" -> "*MC.%7E-_*Periodical-"}, { "name" -> "Movie", "word" -> "elephant", "desc" -> "a movie", "input" -> "*MC.%7E-_*Movie-"}, { "name" -> "WordData", "word" -> "", "desc" -> " referring to English words", "input" -> "*MC.%7E-_*WordData-"}}}, { "type" -> "SubCategory", "word" -> "elephant", "template" -> "Assuming ${desc1}. Use ${desc2} instead", "count" -> "2", "Values" -> {{ "name" -> "Family:Elephantidae", "desc" -> "elephants", "input" -> "*DPClash.SpeciesE.elephant-_*Family%\ 3AElephantidae-"}, { "name" -> "Species:LoxodontaAfricana", "desc" -> "Loxodonta africana", "input" -> "*DPClash.SpeciesE.elephant-_*Species%\ 3ALoxodontaAfricana-"}}}}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{135., {7., 16.}}, TrackedSymbols:>{ WolframAlphaClient`Private`query$$, WolframAlphaClient`Private`boxes$$, WolframAlphaClient`Private`allassumptions$$, WolframAlphaClient`Private`assumptions$$, WolframAlphaClient`Private`open$$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{WolframAlphaClient`Private`open$$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)

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\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "picture of Einstein", WolframAlphaClient`Private`boxes$$ = RowBox[{"EntityValue", "[", RowBox[{ TemplateBox[{"\"Albert Einstein\"", RowBox[{"Entity", "[", RowBox[{"\"Person\"", ",", "\"AlbertEinstein::6tb7g\""}], "]"}], "\"Entity[\\\"Person\\\", \\\"AlbertEinstein::6tb7g\\\"]\"", "\"person\""}, "Entity"], ",", TemplateBox[{"\"image\"", RowBox[{"EntityProperty", "[", RowBox[{"\"Person\"", ",", "\"Image\""}], "]"}], "\"EntityProperty[\\\"Person\\\", \\\"Image\\\"]\""}, "EntityProperty"]}], "]"}], WolframAlphaClient`Private`allassumptions$$ = {{ "type" -> "Clash", "word" -> "Einstein", "template" -> "Assuming \"${word}\" is ${desc1}. Use as \ ${desc2} instead", "count" -> "3", "Values" -> {{ "name" -> "Person", "desc" -> "a person", "input" -> "*C.Einstein-_*Person-"}, { "name" -> "Book", "desc" -> "a book", "input" -> "*C.Einstein-_*Book-"}, { "name" -> "Satellite", "desc" -> "a spacecraft", "input" -> "*C.Einstein-_*Satellite-"}}}}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{125., {7., 16.}}, TrackedSymbols:>{ WolframAlphaClient`Private`query$$, WolframAlphaClient`Private`boxes$$, WolframAlphaClient`Private`allassumptions$$, WolframAlphaClient`Private`assumptions$$, WolframAlphaClient`Private`open$$}], DynamicModuleValues:>{}, UndoTrackedVariables:>{WolframAlphaClient`Private`open$$}], BaseStyle->{"Deploy"}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)

Run the code to distort the image. Try different numbers to get different effects:

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Geometric image transformations distort images. The distortion is given by a pure function, indicated by # and &:

A sine function (Sin) gives a rippling effect, like a reflection in water:

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Create an interface to make the distortion interactive. Drag the slider to make the image ripple:

SHOW/HIDE DETAILS

Here is an expression for a transformed image:

ImageTransformation[\!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxkvHd0XVWe/SnnTM5UFQUUqYDCYGycs2zZyjnHl3POOecc9ZSDZUkOYKAA 4xyUbbpnuqenumzLypJtqrp79Zr/Z993jYtf91qbs849NzzpfO7+hmebN5sE RfTlGRkZkrUYihoVB8TiRlXxMzgo5UtYDD6NeowvpTFo4u1NK7Aown9x/EfM aefnmReXGBcWMWFcnGddXmRemmP8OEPO2VcWOJcfi4vx0jzv+iMscq8tca4u QryrS9wri6Ibj3jXH2CRf+Oh4OYD4fADwdACRvHoI+H1RfHwQ8HQEg5FIw+F N5fENx+Iri1IR3+GJCOPIOnwY0mGHspGfsYEIymsQFjRDP9NOfyzDIfDS9LR h+kbccHf5KN/xygdxl3EITmXDD1Kz39Wjv6N0PDP6tG/q3Dx0M+q0QfqsYea 8UfkqJ34GSLnOEWehRQjS7JRQvKxB08mivGHmEiGFyDp+CMcqseW1BMPFLce KH56qJwgnqAZ+xtEPuTXH6GdeKideKC9tYiR/HTF+JL81jxuh1Sji5pxfPSS YnRedfuBYmKRlPLW0pM5JB9fkI3Nk3NMSDEvLYAg88Ii6+IC+9Ii88I88LEu zmGCkX1p/gk+iH9pAchwyL/2AMKcOLwyJ7i2yL06D5Q4FNxYAiZINPQA+wyC 5CHJCxMSE7CS+AilGZGw/rdIuIqhRwAhH35AEBwhxienfn0lyR0T1djfFSA4 /LNqBDc+xAQiHjKyRIrk9UTY0l+vy4cXIenIIomPFA7BDhOwk4wuqsaXdGPA 8XiTAUJPMv1FgPJrqccW1ePzuD49fygfW5TfWlSOEc8BwTTZJeXYAqiRpDA+ AfdEsuFZUMZZ6egceU0aGUw3B4IQ4b4fZ8CIeWH2McErc9zLc7wr84LLiyCY 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To make the expression interactive, wrap it with Manipulate, replace the value 1 with the variable r, and specify that r ranges from 0 to 25, with an initial value of 0 and label ripple:

Manipulate[ ImageTransformation[\!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxkvHd0XVWe/SnnTM5UFQUUqYDCYGycs2zZyjnHl3POOecc9ZSDZUkOYKAA 4xyUbbpnuqenumzLypJtqrp79Zr/Z993jYtf91qbs849NzzpfO7+hmebN5sE RfTlGRkZkrUYihoVB8TiRlXxMzgo5UtYDD6NeowvpTFo4u1NK7Aown9x/EfM aefnmReXGBcWMWFcnGddXmRemmP8OEPO2VcWOJcfi4vx0jzv+iMscq8tca4u QryrS9wri6Ibj3jXH2CRf+Oh4OYD4fADwdACRvHoI+H1RfHwQ8HQEg5FIw+F N5fENx+Iri1IR3+GJCOPIOnwY0mGHspGfsYEIymsQFjRDP9NOfyzDIfDS9LR h+kbccHf5KN/xygdxl3EITmXDD1Kz39Wjv6N0PDP6tG/q3Dx0M+q0QfqsYea 8UfkqJ34GSLnOEWehRQjS7JRQvKxB08mivGHmEiGFyDp+CMcqseW1BMPFLce KH56qJwgnqAZ+xtEPuTXH6GdeKideKC9tYiR/HTF+JL81jxuh1Sji5pxfPSS YnRedfuBYmKRlPLW0pM5JB9fkI3Nk3NMSDEvLYAg88Ii6+IC+9Ii88I88LEu zmGCkX1p/gk+iH9pAchwyL/2AMKcOLwyJ7i2yL06D5Q4FNxYAiZINPQA+wyC 5CHJCxMSE7CS+AilGZGw/rdIuIqhRwAhH35AEBwhxienfn0lyR0T1djfFSA4 /LNqBDc+xAQiHjKyRIrk9UTY0l+vy4cXIenIIomPFA7BDhOwk4wuqsaXdGPA 8XiTAUJPMv1FgPJrqccW1ePzuD49fygfW5TfWlSOEc8BwTTZJeXYAqiRpDA+ 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HIDE DETAILS
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Add controls for the strength and frequency of the ripple. Adjust the controls to find a good ripple effect:

SHOW/HIDE DETAILS

Add a strength control by replacing .02 with the variable s, and let s range from 0 to .1 with an initial value of .02 and label strength. Appearance->Labeled puts a label on the slider so you can see its value:

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Add a frequency control in the same way.

HIDE DETAILS
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Make a list of animation frames. Change .03 and 20 to the values of strength and frequency you found in the previous step:

SHOW/HIDE DETAILS

To make an animated GIF, you need a list of the GIFs frames. Use Table to make the list.

This Table expression makes a list of the values of r as it goes from 0 to 6 in steps of .5:

Table[r, {r, 0, 6, .5}]

Here is a similar Table expression that gives a list of distorted images where the ripple goes from 0 to 6 in steps of Pi/6:

Table[ ImageTransformation[\!\(\* GraphicsBox[ TagBox[RasterBox[CompressedData[" 1:eJxkvHd0XVWe/SnnTM5UFQUUqYDCYGycs2zZyjnHl3POOecc9ZSDZUkOYKAA 4xyUbbpnuqenumzLypJtqrp79Zr/Z993jYtf91qbs849NzzpfO7+hmebN5sE RfTlGRkZkrUYihoVB8TiRlXxMzgo5UtYDD6NeowvpTFo4u1NK7Aown9x/EfM aefnmReXGBcWMWFcnGddXmRemmP8OEPO2VcWOJcfi4vx0jzv+iMscq8tca4u QryrS9wri6Ibj3jXH2CRf+Oh4OYD4fADwdACRvHoI+H1RfHwQ8HQEg5FIw+F N5fENx+Iri1IR3+GJCOPIOnwY0mGHspGfsYEIymsQFjRDP9NOfyzDIfDS9LR h+kbccHf5KN/xygdxl3EITmXDD1Kz39Wjv6N0PDP6tG/q3Dx0M+q0QfqsYea 8UfkqJ34GSLnOEWehRQjS7JRQvKxB08mivGHmEiGFyDp+CMcqseW1BMPFLce KH56qJwgnqAZ+xtEPuTXH6GdeKideKC9tYiR/HTF+JL81jxuh1Sji5pxfPSS YnRedfuBYmKRlPLW0pM5JB9fkI3Nk3NMSDEvLYAg88Ii6+IC+9Ii88I88LEu zmGCkX1p/gk+iH9pAchwyL/2AMKcOLwyJ7i2yL06D5Q4FNxYAiZINPQA+wyC 5CHJCxMSE7CS+AilGZGw/rdIuIqhRwAhH35AEBwhxienfn0lyR0T1djfFSA4 /LNqBDc+xAQiHjKyRIrk9UTY0l+vy4cXIenIIomPFA7BDhOwk4wuqsaXdGPA 8XiTAUJPMv1FgPJrqccW1ePzuD49fygfW5TfWlSOEc8BwTTZJeXYAqiRpDA+ AfdEsuFZUMZZ6egceU0aGUw3B4IQ4b4fZ8CIeWH2McErc9zLc7wr84LLiyCY 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HIDE DETAILS
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