Jan Trávník

Tupper did eventually make a genuinely self-referential formula. Trávník has made a very impressive one with a smooth typeface. https://jtra.cz/stuff/essays/math-self-reference-smooth/index.html

I also like the simplified Common Lisp reference: https://jtra.cz/stuff/lisp/sclr/index.html

The full text search feature is surprisingly useful. Just searched my ~800 books for keywords like "tree traversal" or "assoc" to find books that I wouldn't have suspected to deal with these topics (`assoc` being a Lisp keyword searching for entries in association lists [1]). And I already had ways to search within contents of my books via "HoudahSpot" (an excelent MacOS tool that uses Spotlight search to sift through all my files and present the results in a tabular view), or via command line using `mdfind` [2] [1] https://jtra.cz/stuff/lisp/sclr/assoc.html [2] For example searching all PDF files for a certain keyword: mdfind "kMDItemKind='*PDF*' && kMDItemTextContent='*tree-traversal*'" | grep -Ev "Mail|Library" | sort | less

This is a better version: https://jtra.cz/stuff/essays/math-self-reference/index.html (it actually contains the entirety of the description of what to plot. Also there's an updated version which uses bezier curves for a smooth output)

http://jtra.cz/stuff/essays/bokeh/ here's an extremely in depth look at what that means. It explains what people mean by "soft bokeh" (~= bokehlicious!), apodized lenses, and the "cat's eye" shit you find sometimes.

Then you may be interested in Jakub Trávník's self referential formula: http://jtra.cz/stuff/essays/math-self-reference/index.html

You may enjoy this then: http://jtra.cz/stuff/essays/math-self-reference/index.html

You have let [0], why would you need a special loop function? [0] http://jtra.cz/stuff/lisp/sclr/let.html Edit: That is to say, this is a simplified reference, and loop is a macro, not a special form.

Jakub Travnik has a better version where the image includes the necessary constant. http://jtra.cz/stuff/essays/math-self-reference/index.html

Sorry, it ain't self-referential unless it draws the picture around (0, 0). I have no idea if that's possible, though. Quines are possible in many programming languages, but the "language" of formulas without quantifiers is very limited. You can encode boolean logic, not sure about loops. EDIT: After some Googling, I've found a true self-referential formula: http://jtra.cz/stuff/essays/math-self-reference/index.html Note that it involves a recursive function definition, and part of the formula is generated by a fixpoint trick. I suppose that's the simplest way to do this. Also I really enjoyed the way he embedded a watermark into the formula, in a way that's difficult to remove if you don't know what you're doing.

Interesting, by looking up mapcan, I came across the Simplified Lisp Reference: http://jtra.cz/stuff/lisp/sclr/mapcan.html Also linked from the resources-section of: http://gettingstartedwithcommonlisp.com/ I don't think I've come across the simplified reference before -- appears to be a good resource for those of us starting out with lisp -- striking a balance between all of CLOS and the sometimes simplistic presentation of text books.

Yes! To both. Calling Tupper's formula "self-referential" (which he did not) is essentially cheating: https://shreevatsa.wordpress.com/2011/04/12/how-does-tuppers-self-refe… But someone has made one where the output contains everything: http://jtra.cz/stuff/essays/math-self-reference/ A little discussion on Reddit: http://www.reddit.com/r/math/comments/i75t1/tuppers_formula_popular_to…

in [1]: "Now, this simulation above may look too artificial and unintuitive. Real lenses do not behave like this, right? They actually do. Just look at this picture below." So he produces an accurate convolution model of how bokeh looks in soft/hard configurations, and that's proof it's not easily simulated? If it's not a straight Gaussian blur (as the HTC is likely using), that's fine - it can still be simulated. What plenoptic cameras do is use a microlens array to perform focus bracketing. One can use a macrolens array as well, if one lives in a rich enough 3D-interpolating image processing pipeline. Take a brick-sized lump of plastic, apply, say, 20 tiny cameras (each of four corners and center get a sub-array of medium_NIR_filtered-far-medium-near), and four temporally staggered Kinect structured light projectors on side, and you get all your cues double-checked by redundant information. Your algorithms get to play with direct low-resolution texture-focus info, stereo distance for a bunch of long-baseline pairs in two dimensions, redundant short-baseline pairs, active focus returns on laser dots as an anchor, stereo returns on laser dots, everything. One checkerboard calibration and such a system cross-calibrates itself and characterizes a position, focus, & lens distortion model for every lens. Add additional lenses if you want to play with more of or some other type of bracketting. The point is, attempting proper computer vision scene capture involves a…

As a programmer who also happens to be a photographer, that's flat out wrong. The M8 produces a very crappy imitation of out of focus blur of what the bokeh of an camera with a thin depth of field looks like. [1] The linked article is actually being "neutral" and fairly generous; the pictures, frankly, look like shit. It is difficult to properly do DoF, even if you know the Z-distance of every object in the scene. It's not just a simple blur of things that are deemed out of focus; things like spherical differences in the lens to produce hard/soft bokeh matter. [2] "So easily simulated" couldn't be further from the truth. A bunch of academic papers have been written about this, [3] which include ways to reproduce effects that are similar to the "thin DoF" effect in large sensor cameras, but few try to tackle _all_ of the issues and nuances present. [1] http://www.trustedreviews.com/opinions/htc-one-m8-camera-vs-a-proper-c… [2] http://jtra.cz/stuff/essays/bokeh/ [3] http://dl.acm.org/citation.cfm?id=2389316.2389318