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August 29, 2015 14:25
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16x16 Mandelbrot set rendered by a tint transform (it's not technically a valid pdf because it lacks lengths and the xref table which is hard to write by hand, but every reader can reconstruct them anyways). The Mandelbrot16x16-fixed.pdf file has been opened and saved with Adobe Reader which repairs the file (but makes it human unreadable).
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| << /Type /Catalog | |
| /Outlines 2 0 R | |
| /Pages 3 0 R | |
| >> | |
| endobj | |
| 2 0 obj | |
| << /Type Outlines | |
| /Count 0 | |
| >> | |
| endobj | |
| 3 0 obj | |
| << /Type /Pages | |
| /Kids [ 4 0 R ] | |
| /Count 1 | |
| >> | |
| endobj | |
| 4 0 obj | |
| << | |
| /Type /Page | |
| /Parent 3 0 R | |
| /MediaBox [ 0 0 100 100 ] | |
| /Contents 5 0 R | |
| /Resources << | |
| /ProcSet 6 0 R | |
| /XObject << | |
| /Im1 7 0 R >> | |
| >> | |
| >> | |
| endobj | |
| 7 0 obj | |
| << /Type /XObject | |
| /Subtype /Image | |
| /Width 16 | |
| /Height 16 | |
| /ColorSpace [/Separation /Mandelbrot /DeviceGray 8 0 R] | |
| /BitsPerComponent 8 | |
| /Length null | |
| /Filter /ASCIIHexDecode >> | |
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| 5 0 obj | |
| << /Length null >> %page content | |
| stream | |
| q % Save graphics state | |
| 100 0 0 100 0 0 cm % Translate to (0,0) and scale by 100 | |
| /Im1 Do % Paint image | |
| Q % Restore graphics state | |
| endstream | |
| endobj | |
| 8 0 obj | |
| << /FunctionType 4 | |
| /Domain [ 0.0 1.0 ] | |
| /Range [ 0.0 1.0 ] | |
| /Length null | |
| >> | |
| stream | |
| { | |
| 255 mul % scale input | |
| round | |
| dup % make a copy of the input | |
| % get upper nibble | |
| -4 bitshift % >> 4 | |
| 7.5 sub % -7.5 .. 7.5 | |
| 5 div % -1.5 .. 1.5 | |
| exch % original (scaled) input to top of stack | |
| % get lower nibble | |
| 16 mod % "and" is broken in sumatra... | |
| 7.5 sub % -7.5 .. 7.5 | |
| 5 div % -1.5 .. 1.5 | |
| % Stack: Re, Im | |
| 2 copy % c: (Re, Im), z:(Re, Im) | |
| 0 1 eq | |
| % ITERATION START | |
| % stack : stop, Re, Im, Re(c), Im(c) | |
| {1 1 eq} { | |
| % Calculate: z^2 + c: (Re(z)^2 - Im(z)^2 + Re(c), 2*Re*Im + Im(c)) | |
| dup dup mul % stack : Re^2, Re, Im, ... | |
| 2 index % stack: Im, Re^2, Re, Im, ... | |
| dup mul % stack: Im^2, Re^2, Re, Im, ... | |
| sub %stack: Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| 3 index % stack: Re(c), Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| add % stack: Re^2 - Im^2 + Re(c), Re, Im, Re(c), Im(c) | |
| 3 1 roll % stack: Re, Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| mul % stack: Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 2 mul % stack: 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 3 index % stack: Im(c), 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| add % stack: 2*Re*Im + Im(c), Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| exch % stack: Re^2 - Im^2 + Re(c), 2*Re*Im + Im(c), Re(c), Im(c) | |
| % stack: Re, Im, Re(c), Im(c) | |
| % Check |z| >= 2: sqrt(Re^2 + Im^2) >= 2 | |
| dup dup mul % stack: Re^2, Re, Im, Re(c), Im(c) | |
| 2 index % stack: Im, Re^2, Re, Im, Re(c), Im(c) | |
| dup mul % stack: Im^2, Re^2, Re, Im, Re(c), Im(c) | |
| add % stack: Im^2 + Re^2, Re, Im, Re(c), Im(c) | |
| sqrt % stack: sqrt(Im^2 + Re^2), Re, Im, Re(c), Im(c) | |
| 2 ge % stack: stop, Re, Im, Re(c), Im(c) | |
| } ifelse | |
| {1 1 eq} { | |
| % Calculate: z^2 + c: (Re(z)^2 - Im(z)^2 + Re(c), 2*Re*Im + Im(c)) | |
| dup dup mul % stack : Re^2, Re, Im, ... | |
| 2 index % stack: Im, Re^2, Re, Im, ... | |
| dup mul % stack: Im^2, Re^2, Re, Im, ... | |
| sub %stack: Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| 3 index % stack: Re(c), Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| add % stack: Re^2 - Im^2 + Re(c), Re, Im, Re(c), Im(c) | |
| 3 1 roll % stack: Re, Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| mul % stack: Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 2 mul % stack: 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 3 index % stack: Im(c), 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| add % stack: 2*Re*Im + Im(c), Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| exch % stack: Re^2 - Im^2 + Re(c), 2*Re*Im + Im(c), Re(c), Im(c) | |
| % stack: Re, Im, Re(c), Im(c) | |
| % Check |z| >= 2: sqrt(Re^2 + Im^2) >= 2 | |
| dup dup mul % stack: Re^2, Re, Im, Re(c), Im(c) | |
| 2 index % stack: Im, Re^2, Re, Im, Re(c), Im(c) | |
| dup mul % stack: Im^2, Re^2, Re, Im, Re(c), Im(c) | |
| add % stack: Im^2 + Re^2, Re, Im, Re(c), Im(c) | |
| sqrt % stack: sqrt(Im^2 + Re^2), Re, Im, Re(c), Im(c) | |
| 2 ge % stack: stop, Re, Im, Re(c), Im(c) | |
| } ifelse | |
| {1 1 eq} { | |
| % Calculate: z^2 + c: (Re(z)^2 - Im(z)^2 + Re(c), 2*Re*Im + Im(c)) | |
| dup dup mul % stack : Re^2, Re, Im, ... | |
| 2 index % stack: Im, Re^2, Re, Im, ... | |
| dup mul % stack: Im^2, Re^2, Re, Im, ... | |
| sub %stack: Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| 3 index % stack: Re(c), Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| add % stack: Re^2 - Im^2 + Re(c), Re, Im, Re(c), Im(c) | |
| 3 1 roll % stack: Re, Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| mul % stack: Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 2 mul % stack: 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 3 index % stack: Im(c), 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| add % stack: 2*Re*Im + Im(c), Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| exch % stack: Re^2 - Im^2 + Re(c), 2*Re*Im + Im(c), Re(c), Im(c) | |
| % stack: Re, Im, Re(c), Im(c) | |
| % Check |z| >= 2: sqrt(Re^2 + Im^2) >= 2 | |
| dup dup mul % stack: Re^2, Re, Im, Re(c), Im(c) | |
| 2 index % stack: Im, Re^2, Re, Im, Re(c), Im(c) | |
| dup mul % stack: Im^2, Re^2, Re, Im, Re(c), Im(c) | |
| add % stack: Im^2 + Re^2, Re, Im, Re(c), Im(c) | |
| sqrt % stack: sqrt(Im^2 + Re^2), Re, Im, Re(c), Im(c) | |
| 2 ge % stack: stop, Re, Im, Re(c), Im(c) | |
| } ifelse | |
| {1 1 eq} { | |
| % Calculate: z^2 + c: (Re(z)^2 - Im(z)^2 + Re(c), 2*Re*Im + Im(c)) | |
| dup dup mul % stack : Re^2, Re, Im, ... | |
| 2 index % stack: Im, Re^2, Re, Im, ... | |
| dup mul % stack: Im^2, Re^2, Re, Im, ... | |
| sub %stack: Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| 3 index % stack: Re(c), Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| add % stack: Re^2 - Im^2 + Re(c), Re, Im, Re(c), Im(c) | |
| 3 1 roll % stack: Re, Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| mul % stack: Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 2 mul % stack: 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 3 index % stack: Im(c), 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| add % stack: 2*Re*Im + Im(c), Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| exch % stack: Re^2 - Im^2 + Re(c), 2*Re*Im + Im(c), Re(c), Im(c) | |
| % stack: Re, Im, Re(c), Im(c) | |
| % Check |z| >= 2: sqrt(Re^2 + Im^2) >= 2 | |
| dup dup mul % stack: Re^2, Re, Im, Re(c), Im(c) | |
| 2 index % stack: Im, Re^2, Re, Im, Re(c), Im(c) | |
| dup mul % stack: Im^2, Re^2, Re, Im, Re(c), Im(c) | |
| add % stack: Im^2 + Re^2, Re, Im, Re(c), Im(c) | |
| sqrt % stack: sqrt(Im^2 + Re^2), Re, Im, Re(c), Im(c) | |
| 2 ge % stack: stop, Re, Im, Re(c), Im(c) | |
| } ifelse | |
| {1 1 eq} { | |
| % Calculate: z^2 + c: (Re(z)^2 - Im(z)^2 + Re(c), 2*Re*Im + Im(c)) | |
| dup dup mul % stack : Re^2, Re, Im, ... | |
| 2 index % stack: Im, Re^2, Re, Im, ... | |
| dup mul % stack: Im^2, Re^2, Re, Im, ... | |
| sub %stack: Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| 3 index % stack: Re(c), Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| add % stack: Re^2 - Im^2 + Re(c), Re, Im, Re(c), Im(c) | |
| 3 1 roll % stack: Re, Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| mul % stack: Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 2 mul % stack: 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 3 index % stack: Im(c), 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| add % stack: 2*Re*Im + Im(c), Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| exch % stack: Re^2 - Im^2 + Re(c), 2*Re*Im + Im(c), Re(c), Im(c) | |
| % stack: Re, Im, Re(c), Im(c) | |
| % Check |z| >= 2: sqrt(Re^2 + Im^2) >= 2 | |
| dup dup mul % stack: Re^2, Re, Im, Re(c), Im(c) | |
| 2 index % stack: Im, Re^2, Re, Im, Re(c), Im(c) | |
| dup mul % stack: Im^2, Re^2, Re, Im, Re(c), Im(c) | |
| add % stack: Im^2 + Re^2, Re, Im, Re(c), Im(c) | |
| sqrt % stack: sqrt(Im^2 + Re^2), Re, Im, Re(c), Im(c) | |
| 2 ge % stack: stop, Re, Im, Re(c), Im(c) | |
| } ifelse | |
| {1 1 eq} { | |
| % Calculate: z^2 + c: (Re(z)^2 - Im(z)^2 + Re(c), 2*Re*Im + Im(c)) | |
| dup dup mul % stack : Re^2, Re, Im, ... | |
| 2 index % stack: Im, Re^2, Re, Im, ... | |
| dup mul % stack: Im^2, Re^2, Re, Im, ... | |
| sub %stack: Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| 3 index % stack: Re(c), Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| add % stack: Re^2 - Im^2 + Re(c), Re, Im, Re(c), Im(c) | |
| 3 1 roll % stack: Re, Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| mul % stack: Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 2 mul % stack: 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 3 index % stack: Im(c), 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| add % stack: 2*Re*Im + Im(c), Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| exch % stack: Re^2 - Im^2 + Re(c), 2*Re*Im + Im(c), Re(c), Im(c) | |
| % stack: Re, Im, Re(c), Im(c) | |
| % Check |z| >= 2: sqrt(Re^2 + Im^2) >= 2 | |
| dup dup mul % stack: Re^2, Re, Im, Re(c), Im(c) | |
| 2 index % stack: Im, Re^2, Re, Im, Re(c), Im(c) | |
| dup mul % stack: Im^2, Re^2, Re, Im, Re(c), Im(c) | |
| add % stack: Im^2 + Re^2, Re, Im, Re(c), Im(c) | |
| sqrt % stack: sqrt(Im^2 + Re^2), Re, Im, Re(c), Im(c) | |
| 2 ge % stack: stop, Re, Im, Re(c), Im(c) | |
| } ifelse | |
| {1 1 eq} { | |
| % Calculate: z^2 + c: (Re(z)^2 - Im(z)^2 + Re(c), 2*Re*Im + Im(c)) | |
| dup dup mul % stack : Re^2, Re, Im, ... | |
| 2 index % stack: Im, Re^2, Re, Im, ... | |
| dup mul % stack: Im^2, Re^2, Re, Im, ... | |
| sub %stack: Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| 3 index % stack: Re(c), Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| add % stack: Re^2 - Im^2 + Re(c), Re, Im, Re(c), Im(c) | |
| 3 1 roll % stack: Re, Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| mul % stack: Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 2 mul % stack: 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 3 index % stack: Im(c), 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| add % stack: 2*Re*Im + Im(c), Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| exch % stack: Re^2 - Im^2 + Re(c), 2*Re*Im + Im(c), Re(c), Im(c) | |
| % stack: Re, Im, Re(c), Im(c) | |
| % Check |z| >= 2: sqrt(Re^2 + Im^2) >= 2 | |
| dup dup mul % stack: Re^2, Re, Im, Re(c), Im(c) | |
| 2 index % stack: Im, Re^2, Re, Im, Re(c), Im(c) | |
| dup mul % stack: Im^2, Re^2, Re, Im, Re(c), Im(c) | |
| add % stack: Im^2 + Re^2, Re, Im, Re(c), Im(c) | |
| sqrt % stack: sqrt(Im^2 + Re^2), Re, Im, Re(c), Im(c) | |
| 2 ge % stack: stop, Re, Im, Re(c), Im(c) | |
| } ifelse | |
| {1 1 eq} { | |
| % Calculate: z^2 + c: (Re(z)^2 - Im(z)^2 + Re(c), 2*Re*Im + Im(c)) | |
| dup dup mul % stack : Re^2, Re, Im, ... | |
| 2 index % stack: Im, Re^2, Re, Im, ... | |
| dup mul % stack: Im^2, Re^2, Re, Im, ... | |
| sub %stack: Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| 3 index % stack: Re(c), Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| add % stack: Re^2 - Im^2 + Re(c), Re, Im, Re(c), Im(c) | |
| 3 1 roll % stack: Re, Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| mul % stack: Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 2 mul % stack: 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 3 index % stack: Im(c), 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| add % stack: 2*Re*Im + Im(c), Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| exch % stack: Re^2 - Im^2 + Re(c), 2*Re*Im + Im(c), Re(c), Im(c) | |
| % stack: Re, Im, Re(c), Im(c) | |
| % Check |z| >= 2: sqrt(Re^2 + Im^2) >= 2 | |
| dup dup mul % stack: Re^2, Re, Im, Re(c), Im(c) | |
| 2 index % stack: Im, Re^2, Re, Im, Re(c), Im(c) | |
| dup mul % stack: Im^2, Re^2, Re, Im, Re(c), Im(c) | |
| add % stack: Im^2 + Re^2, Re, Im, Re(c), Im(c) | |
| sqrt % stack: sqrt(Im^2 + Re^2), Re, Im, Re(c), Im(c) | |
| 2 ge % stack: stop, Re, Im, Re(c), Im(c) | |
| } ifelse | |
| {1 1 eq} { | |
| % Calculate: z^2 + c: (Re(z)^2 - Im(z)^2 + Re(c), 2*Re*Im + Im(c)) | |
| dup dup mul % stack : Re^2, Re, Im, ... | |
| 2 index % stack: Im, Re^2, Re, Im, ... | |
| dup mul % stack: Im^2, Re^2, Re, Im, ... | |
| sub %stack: Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| 3 index % stack: Re(c), Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| add % stack: Re^2 - Im^2 + Re(c), Re, Im, Re(c), Im(c) | |
| 3 1 roll % stack: Re, Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| mul % stack: Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 2 mul % stack: 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 3 index % stack: Im(c), 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| add % stack: 2*Re*Im + Im(c), Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| exch % stack: Re^2 - Im^2 + Re(c), 2*Re*Im + Im(c), Re(c), Im(c) | |
| % stack: Re, Im, Re(c), Im(c) | |
| % Check |z| >= 2: sqrt(Re^2 + Im^2) >= 2 | |
| dup dup mul % stack: Re^2, Re, Im, Re(c), Im(c) | |
| 2 index % stack: Im, Re^2, Re, Im, Re(c), Im(c) | |
| dup mul % stack: Im^2, Re^2, Re, Im, Re(c), Im(c) | |
| add % stack: Im^2 + Re^2, Re, Im, Re(c), Im(c) | |
| sqrt % stack: sqrt(Im^2 + Re^2), Re, Im, Re(c), Im(c) | |
| 2 ge % stack: stop, Re, Im, Re(c), Im(c) | |
| } ifelse | |
| {1 1 eq} { | |
| % Calculate: z^2 + c: (Re(z)^2 - Im(z)^2 + Re(c), 2*Re*Im + Im(c)) | |
| dup dup mul % stack : Re^2, Re, Im, ... | |
| 2 index % stack: Im, Re^2, Re, Im, ... | |
| dup mul % stack: Im^2, Re^2, Re, Im, ... | |
| sub %stack: Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| 3 index % stack: Re(c), Re^2 - Im^2, Re, Im, Re(c), Im(c) | |
| add % stack: Re^2 - Im^2 + Re(c), Re, Im, Re(c), Im(c) | |
| 3 1 roll % stack: Re, Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| mul % stack: Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 2 mul % stack: 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| 3 index % stack: Im(c), 2*Re*Im, Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| add % stack: 2*Re*Im + Im(c), Re^2 - Im^2 + Re(c), Re(c), Im(c) | |
| exch % stack: Re^2 - Im^2 + Re(c), 2*Re*Im + Im(c), Re(c), Im(c) | |
| % stack: Re, Im, Re(c), Im(c) | |
| % Check |z| >= 2: sqrt(Re^2 + Im^2) >= 2 | |
| dup dup mul % stack: Re^2, Re, Im, Re(c), Im(c) | |
| 2 index % stack: Im, Re^2, Re, Im, Re(c), Im(c) | |
| dup mul % stack: Im^2, Re^2, Re, Im, Re(c), Im(c) | |
| add % stack: Im^2 + Re^2, Re, Im, Re(c), Im(c) | |
| sqrt % stack: sqrt(Im^2 + Re^2), Re, Im, Re(c), Im(c) | |
| 2 ge % stack: stop, Re, Im, Re(c), Im(c) | |
| } ifelse | |
| {1} {0} ifelse | |
| } | |
| endstream | |
| endobj | |
| 6 0 obj %procset | |
| [ /PDF ] | |
| endobj | |
| trailer | |
| << /Size 7 | |
| /Root 1 0 R | |
| >> | |
| %%EOF |
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