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Benoit Mandelbrot Dies At 85

Soulskill posted more than 4 years ago | from the edges-are-interesting dept.

Math 131

Beetle B. writes "Benoit Mandelbrot has passed away at the age of 85. I first learned of the Mandelbrot set while reading Arthur C. Clarke's The Ghost From The Grand Banks. Soon after, I got hold of the best fractal generation software of the day — Fractint — and ran it for long periods of time on my XT, exploring the beautiful world that Mandelbrot, among others, had opened up for me. That it was only on a 4-color CGA did not deter me!"

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From Life ... (3, Funny)

Mikkeles (698461) | more than 4 years ago | (#33917884)

to the Hausdorf Dimension!

Fractal mathematicians don't die (1)

JamesP (688957) | more than 4 years ago | (#33918244)

The keep splitting themselves into even fractionally dimensioned smaller pieces

Re:Fractal mathematicians don't die (-1, Redundant)

Anonymous Coward | more than 4 years ago | (#33918360)

I am not a Christian. In my discussions of this fact with Christians, I have repeatedly run into one major misunderstanding. The Christians assume that if I believed the Bible were true, I would become a Christian; that is, they believe that my reason for not being a Christian is that I don't believe in their god. This is not the case.

One disclaimer: The thesis of this essay is that even if a God as described in the Bible does exist, he is not fit for worship due to his low moral standards. Consequently, I speak sometimes as if I did believe the Bible, when in fact I do not.

If I had undeniable proof of the existence of Yahweh, aka Jehovah, aka Adonai, aka El Shaddai, aka Yahweh Elohim, the father of Jesus and the ancient leader of the Semitic peoples, I still would not worship the bastard. If an angel appeared to me and removed my appendectomy scar so I could never deny the reality of divine power, I still would not be a Christian. My primary reason for not being a Christian or Jew has nothing to do with my lack of belief in their god. My primary reason is that the Bible is a disgusting book describing the behavior of a god without the morality of an average high school student.

That God does what he wants, when he wants, without even an attempt at self-justification, and all for what reason? According to Paul, all for his own greater glory. Oh, how charming. For his own glory he condemns billions to eternal torment, drowns millions of innocent beasts and thousands of children, orders the slaughter of entire cities down to the last man, woman, and child, creates a race that he knows is flawed and will hurt itself (so that in their pain they can worship him better), refuses to deal with any other god on a friendly basis, restricts the normal expression of the sexual function, rains doom on those who dare to try to be as knowledgable as he is, and so on.

Jesus preaching love in no way atones for these many hideous crimes; lest we forget, it was at the time of Jesus that he created Hell. This cruellest of all concentration camps (certainly far worse than the ones created by the Nazis) was at no time mentioned in the Old Testament, and the wrathful and threatening god of the Old Testament would hardly have omitted any chance to terrify his worshippers.

I have heard some Christians who believe that there is no everburning Hell in their religion, that the "lake of fire" is purely destructive, that sinners will be annihilated rather than tortured after the Last Judgment. Sometimes, they claim that medieval Catholics created that "myth", and that they would revile any god who made this concentration camp.

Well, get ready to start reviling then. The myth of Hell was not created in the Middle Ages. It is explicitly stated in a set of books called the Synoptic Gospels, you know, the ones by Matthew, Mark, and Luke. Since some people don't seem to be very familiar with these books, usually considered the cornerstone of Christianity, I'll fill them in.

Matthew 18:8-9 has Jesus saying, "If your hand or your foot should cause you to sin, cut it off and throw it away: it is better for you to enter into life crippled or lame, than to have two hands or two feet and be thrown into eternal fire." A little while later, in 18:34-35 to be exact, Jesus finishes up a parable about an unforgiving debtor with: "And in his anger the master handed him over to the torturers till he should pay all his debt. And that is how my heavenly Father will deal with you unless you each forgive your brother from your heart." Not clean killing -- you will be handed over to the torturers. In the parable of the wedding feast, Matthew 22:1-14, Jesus concludes with "Then the king said to the attendants, 'Bind him hand and foot and throw him out into the dark, where there will be weeping and grinding of teeth.'" The king didn't say, "Execute him", but bind him and throw him into a painful place. This is echoed in Mat. 24:51, in almost the same words, and again in Mat. 25:30, again with similar words. Finally (for Matthew), we have Mat. 25:41-46, on the Last Judgment. "Next he will say to those on his left hand, 'Go away from me, with your curse upon you, to the eternal fire prepared for the devil and his angels... And they will go away to eternal punishment, and the virtuous to eternal life.'" My point is proven, so I won't bore you with the quotes from Mark and Luke; however, check out Mark 9:43, Mark 9:48-49, Luke 13:27-28, and Luke 16:23-26 if you still doubt.

You hear a lot from Christians about Yahweh's "infinite compassion and mercy". Tell it to the Midianites. Numbers 31 is a classic example of wholesale slaughter and rape under the direction of Yahweh. A sample of this delightful tale: "They waged the campaign against Midian, as Yahweh had ordered Moses, and they put every male to death.... The sons of Israel took the Midianite women captive with their young children, and plundered all their cattle, all their flocks and all their goods. They set fire to the towns where they lived and all their encampments.... Moses was enraged with the commanders of the army ... who had come back from this military expedition. He said, 'Why have you spared the life of all the women? ... So kill all the male children. Kill also all the women who have slept with a man. Spare the lives only of the young girls who have not slept with a man, and take them for yourselves.'" Yes, friends, this is infinite mercy and compassion for you. I particularly like the way that Moses got upset with them for sparing women and male children, but allowed the young girls to be kept for later raping. If only humans could keep to such lofty standards without the necessity of divine revelation.

I could go on for quite a while in this vein. I don't think the firstborn in Egypt during the captivity would have agreed with the verdict of compassion and mercy (Ex. 11:5,12:29), particularly since it was due to Yahweh's hardening of Pharoah's heart in the first place that made this neccessary. Also, with omnipotence, Yahweh could have teleported the Jews out of captivity without bloodshed, or put the Egyptians to sleep while they left, but no. That wouldn't be gory and exciting enough for him.

Then there are the charming instructions about women taken in war, from Deut. 21:10-14. And there is Deuteronomy 28:20-46, a long stream of invectives and curses straight from the prophet's mouth, all about the nasty things Yahweh will do if you upset him a tad. The entire book of Joshua is a long sequence of atrocities. I have not given all these quotes for space reasons -- I urge you to look them up for yourself. If you are not shocked, then your moral standards must be low indeed.

Of course, you will sometimes hear rationalizations of this slaughter. There are two major forms: the corruption argument and the mercy argument. The former says that those slaughtered were evil and deserving of their fate; the latter says that since they were religiously incorrect, it was a mercy to terminate their existence.

The corruption argument simply does not hold up. The people slaughtered in the Old Testament were almost uniformly blameless (with a few exceptions, of course -- for instance, the Sodomites violated the conventions of hospitality.) Usually, no justification is offered beyond the fact that since they were of another tribe, it was OK to kill them. As to the mercy argument: They shoot horses, don't they? However, people are not animals to be destroyed against their will in the name of mercy. If I don't claim to be suffering, and don't ask to die, neither you nor any god has the right to decide that you know better. If you tried to do this to me, I would shoot you; if a god tried, well, the only weapon I would have would be withholding my worship.

Most of us, given omnipotence, would be able to do a far better job than Yahweh. What would you do if given omnipotence? If your answer is anything other than "abolish world hunger", there's something more than a little skewed in your perception of mankind. There is no question that this is the greatest evil in the world today. The second thing would be to abolish disease, right? This doesn't take "infinite mercy", just normal compassion and a bit of common sense. God's supposedly infinite mercy is apparently the same thing as no mercy at all.

What makes this particularly unforgivable is that even Jesus's own standards demand feeding of the poor. See Matthew 26:35, in which it is stated that the blessed feed the hungry, and that the damned do not. Does the old saw about "practicing what you preach" not apply to Yahweh? Is his hypocrisy not a sin?

One popular rationalization of this is that for Yahweh to feed all the hungry would somehow (and it is never explained how) make it more difficult for people to get into Heaven. Sure, and another reason is that it would make the quality of newspapers worse, right? You can't just say that two things are connected when there is no apparent or explained link between them! The charge against Yahweh of infecting us with disease is particularly strong. God made these micro-organisms, and made us subject to them. If I made a bunch of plague germs and set them loose, you would rightly hold me accountable. Since (according to Genesis) all disease comes from Yahweh, I hold him similarly accountable.

Suppose you were a god and there were other gods. What would you do? What I would try to do is the same thing I do as a person among other people -- try to make friends or at least truce with as many of them as possible. The jealous Judeo-Christian god does the opposite.

Some people feel that Yahweh is the only god, and therefore cannot be faulted for not having friendly relations with other gods. This idea is a fairly modern invention: that not only is he the best god, but the only one. Yahweh is repeatedly referred to as "our God" in the Pentateuch, and there is no implication that he is the only real one. Also, try Deut. 5:7-9. It is psychotic to be jealous of nonexistent beings. The statement "You shall have no gods except me" clearly implies that the contrary is possible. Suppose you were an omnipotent god and there were no other gods. What would you do? Perform a continual sequence of verifiable miracles; after all, this doesn't require any effort, and keeps people from delusion. No such luck in the case of Jehovah. He demands absolute fidelity without any demonstration of his existence, beyond some visionary manifestations of the sort that you can get from any religion.

Christians commonly rationalize this in one of two ways. First, they claim that there is a virtue in believing something without proof; that is, faith in itself is held to be a virtue, and Yahweh doesn't want to remove our opportunity to indulge in it. All I can say to this is that I do not consider faith to be a virtue -- I consider it to be a sign of intellectual weakness, and a significant barrier to scientific and other intellectual progress. (I consider scientific progress desirable because it is so efficacious in improving the quality of people's lives.) I see no virtue in accepting a thing on faith, since it may well be false, and it is clearly not a virtue to believe the false. Given the willingness to have faith, how does one decide whether to put it in Christianity instead of Hinduism? There is no way; you just have to cross your fingers and take the plunge. Whichever choice you take, you will hear voices in your head, see divine manifestations, and so on, so even once the plunge is taken there is no way to know you are correct.

Second, there is the rationalization that scientific discovery would become impossible if a continual stream of verifiable miracles were performed. This argument denies the omnipotence of Yahweh. If he can do anything, he can perform a sequence of miracles in such a way as to convince everyone of his existence and not interfere with scientific discovery at all. The only things he can't do are logical absurdities such as making 2+2=5.

The point to remember here is that if we don't believe in him, we go to Hell, and this is a greater evil than a lack of the "virtue" of faith or a stunting of science, or anything else conceivable. If Yahweh is concerned about the good, he will do what he can to keep us from Hell, and keeping vital information from us is the exact opposite of this.

I have heard the claim that Yahweh does not restrict us from learning, that he encourages us to learn all we can. Tell it to the workers at the Tower of Babel. In case your memory fails you here, Gen. 11:6-7 says, "'So they are all a single people with a single language!' said Yahweh. 'This is but the start of their undertakings! There will be nothing too hard for them to do. [ Horrors! -- tim ] Come, let us go down and confuse their language on the spot so that they can no longer understand one another.'" Yahweh deliberately acts to restrict man's capability for understanding.

One thing in particular would keep me from worshipping this god. That is the fact that he desires worship. The only reason why this would be is that he gets something out of worship, perhaps power, perhaps just pleasure. In the former case, it would be totally unjustifiable for me to increase the power of this hugely arrogant and malefic being. In the latter, well, I don't LIKE this deity, and I don't think it deserves such a reward for its heinous career.

Some of the responses I have heard to this sort of argument in the past are shown below, with my answers.

"You can't judge God by the same standards as man." In that case, why is it that I keep getting told that God is good? Are there two meanings of the word "good", one of which forbids murder, deliberate starvation, infecting people with disease, and so on, and another which allows these things? I suggest that there is already a word for the second meaning. That word is "evil". If you think that it's OK to worship an evil god, that's your business, but you can't expect me to do the same.

One particularly curious rationalization here is that "starvation and disease and all the other evils of the world come from breaking God's laws." Starvation comes from not having enough food. Disease comes from exposure to various nasty micro-organisms, and from genetic infirmities. If you can show me how these two things come from breaking god's laws, I will be greatly surprised. Perhaps at the root they are caused by Adam and Eve falling from grace, but you can't hold some starving infant in Namibia responsible for the actions of two long-dead people, any more than you can hold me responsible for the acts of Jack the Ripper. There just isn't sufficient connection to establish guilt.

"Everything God does is really good, even though we can't always see that it is." There is no possible amount of good that can counterbalance the deliberate, perpetual starvation of the human race. Maybe we Americans have it so good that we can't see this, but most of the people in the world are starving. Children are dying by the truckload, not for any sin, but just because there isn't enough food for them. If you could see these children, and you had food, you would give food to them. (Either that, or you are an unfeeling monster.) Not so with the omniscient god you worship. He sees their bellies bloat, sees them run out of nutrients and rot alive, sees their brains dying, and doesn't do a damn thing, despite the fact that he has an unlimited supply of food to give. Another example of his mercy. Christians have been claiming that there will be wonderful events, that will more than make up for the abominable pain and suffering on Earth, for about two thousand years now. It is clear from the gospels that Jesus thought that it was about to happen shortly after his death. Before the Christians, the Zoroastrians were saying it. Yet the world still turns as it has, and there is still no reason to think of these claims as other than pipe-dreams to mollify the masses.

"Don't ask such questions." People who say this are cowering slaves, beneath my notice. They would as soon serve the devil as god in their blindness and faith. No amount of evidence could convince them that the devil was bad once they had decided to worship him; their basic assumption is that they are correct, so they are untouchable by any rationality. In closing, let's see how Yahweh/Jesus stands up to his own standards. In Matthew 26:41-46, we hear the King, "Next he will say to those on his left hand, 'Go away from me, with your curse upon you, to the eternal fire prepared for the devil and his angels. For I was hungry and you never gave me food; I was thirsty and you never gave me anything to drink; I was a stranger and you never made me welcome, naked and you never clothed me, sick and in prison and you never visited me.' ... And they will go away to eternal punishment, and the virtuous to eternal life."

In the light of this, your god himself is the worst of sinners; if there is no double standard, he will be at the head of that line into eternal punishment. He is guilty of every crime of which he accuses the damned. I do not believe in the reality of Jehovah, except as a psychological phenomenon, but if I did believe I would not worship that horror. It could send me to the Hell it's made for those it dislikes, and I would walk in proudly, knowing that I was no slave to be broken down by force.

Re:Fractal mathematicians don't die (4, Funny)

fractoid (1076465) | more than 4 years ago | (#33918834)

Too long, lacks pithiness. Vin Diesel's character, Riddick, put it better in Pitch Black: "Got it all wrong, Holy Man. I absolutely believe in God. And I absolutely hate the fucker." Much more concise.

Re:Fractal mathematicians don't die (2, Funny)

fractoid (1076465) | more than 4 years ago | (#33918824)

Little fleas have lesser fleas upon their backs to bite 'em.
And lesser fleas have smaller fleas, so on ad infinitum.

Re: Fractal mathematicians don't die (2, Funny)

shubert1966 (739403) | more than 4 years ago | (#33920812)

If reincarnation is true, he'll come back as twins.

Fractals are addictive. Like SWINTH for the Commode64, watching a fire, or Hypnotoad.

Re:From Life ... (4, Funny)

Anonymous Coward | more than 4 years ago | (#33918538)

Good luck using Google Maps to zoom in on his graveyard.

Re:From Life ... (3, Funny)

Sulphur (1548251) | more than 4 years ago | (#33919784)

Have you tried Google Maths?

Dead? (4, Insightful)

DarkKnightRadick (268025) | more than 4 years ago | (#33917886)

I didn't know he was still alive. So much for assumptions.

Re:Dead? (4, Informative)

BradleyUffner (103496) | more than 4 years ago | (#33918008)

I didn't know he was still alive. So much for assumptions.

I only knew he was still alive because of this song.
http://www.jonathancoulton.com/songdetails/Mandelbrot%20Set [jonathancoulton.com]

Re:Dead? (3, Informative)

Beorytis (1014777) | more than 4 years ago | (#33918460)

I knew he was still alive because of this TED talk [ted.com]

.

Re:Dead? (1)

Captain Spam (66120) | more than 4 years ago | (#33918784)

I didn't know he was still alive. So much for assumptions.

I only knew he was still alive because of this song.
http://www.jonathancoulton.com/songdetails/Mandelbrot%20Set [jonathancoulton.com]

Cripes, JoCo will need to update that verse of the song. Only, I don't think "Mandelbrot's in Heaven... ... ..." and a long pause, while respectful, would work as well musically.

Of course, he sings an updated version of "Curl" in some of his live shows to account for the fact that the leader of a curling team is the Skip, not the Skipper, so maybe we'll hear a new version soon.

Re:Dead? (4, Funny)

Anonymous Coward | more than 4 years ago | (#33919074)

And if anyone knows about still being alive, it's Jonathan Coulton.

Re:Dead? (1)

DarkKnightRadick (268025) | more than 4 years ago | (#33919762)

He did the Portal song?

Re:Dead? (1)

RichardJenkins (1362463) | more than 4 years ago | (#33919970)

Yes [wikipedia.org]

Re:Dead? (1)

NotQuiteReal (608241) | more than 4 years ago | (#33919184)

I only knew he was dead because of Slashdot - damn you /.!

Re:Dead? (2, Funny)

b4upoo (166390) | more than 4 years ago | (#33918494)

Yes, but he replicates in ever smaller iterations.

Re:Dead? (0)

DarkKnightRadick (268025) | more than 4 years ago | (#33919766)

+1 funny

Re:Dead? (2, Funny)

TapeCutter (624760) | more than 4 years ago | (#33920638)

May he Replicate In Peace

Re:Dead? (0)

Anonymous Coward | more than 4 years ago | (#33919050)

That has been said (*). Not by me.

If you think about some discovery, the discoverer is probably alive -- not dead.

That is due to the accelerating pace of knowledge accumulation.

(*) I wonder if the guy who said this is still alive (it was a 50% alive / 50% dead of the inventors that ever lived, IIRC).

Re:Dead? (0)

DarkKnightRadick (268025) | more than 4 years ago | (#33919776)

Now that's interesting. Should have posted with your name to get some karma. (:

+1 informative for parent

Re:Dead? (1)

nacturation (646836) | more than 4 years ago | (#33919564)

I didn't know he was still alive. So much for assumptions.

This news is quite surreal... almost like it's half real and half imaginary.

Re:Dead? (2, Interesting)

PsychicX (866028) | more than 4 years ago | (#33920026)

He was at our graduation ceremony this past May (Hopkins 10) getting an honorary degree, in fact.

Check out the obit on the New York Times (4, Funny)

Anonymous Coward | more than 4 years ago | (#33917920)

You can use your browser to zoom into it infinitely revealing more patterns.

awesome mind (0)

LiquidCoooled (634315) | more than 4 years ago | (#33917948)

RIP Benoit.
A true genius no longer of this world.

His work has been inspiration to

Re:awesome mind (1, Insightful)

Anonymous Coward | more than 4 years ago | (#33917956)

...

Re:awesome mind (0, Offtopic)

badboy_tw2002 (524611) | more than 4 years ago | (#33918076)

.....

Re:awesome mind (0, Offtopic)

Anonymous Coward | more than 4 years ago | (#33918746)

......

Re:awesome mind (1)

advid.net (595837) | more than 4 years ago | (#33919250)

........

Fractint? Pah? (0)

Anonymous Coward | more than 4 years ago | (#33917954)

Fractint? Back in the early 80s we had to write our own software to draw fractals on our shitty 8 color displays and we had to wait for the results the following morning.

Now get off my lawn.

Re:Fractint? Pah? (2, Insightful)

Anonymous Coward | more than 4 years ago | (#33918032)

Quite - slashdot's obit for a mathematician: read about one thing he did in a popular mass-distributed sci fi book, ran a bit of software (ON A FLOPPY DISK AND ON A FOUR COLOUR DISPLAY!)

Re:Fractint? Pah? (5, Insightful)

Viperpete (1261530) | more than 4 years ago | (#33918238)

I was going to post much the same thing. Some nerd eulogy, 10 words pertaining to the death of a math hero, ~70 devoted to the author. Can we get more HF Asperger/Narcissistic.

Re:Fractint? Pah? (2, Insightful)

Jah-Wren Ryel (80510) | more than 4 years ago | (#33918482)

I was going to post much the same thing. Some nerd eulogy, 10 words pertaining to the death of a math hero, ~70 devoted to the author. Can we get more HF Asperger/Narcissistic.

Yes. How awful that the author would talk about how the deceased affected him personally.
If ever affected as many people as Mandlebrot did, I would be insulted if they talked about it at my funeral.

Re:Fractint? Pah? (0)

Anonymous Coward | more than 4 years ago | (#33919058)

Mandlebrot joy. This is a good thing regardless.

Re:Fractint? Pah? (1)

MK_CSGuy (953563) | more than 4 years ago | (#33920710)

Personally I think it was nice, giving us a perspective how the deceased affected the writer's life, and probably others' as well.

Re:Fractint? Pah? (1)

BluBrick (1924) | more than 4 years ago | (#33920738)

Yes, Fractint. It was my introduction to truly Free Software. Because the group that released it called themselves Stone Soup Software, and I knew the story of Stone Soup, I immediately understood what Free Software was all about.

I always remember this little snippet from one of the many text files that accompanied the archive:

Don't want money, got money. Want admiration.

Re:Fractint? Pah? (2, Informative)

nurb432 (527695) | more than 4 years ago | (#33920854)

Real men did it with checkerboards. In the 80's i had an ST, so i was not trapped in 8-bit color land. But the overnight thing, i totally agree.

From his February 2010 TED visit (4, Informative)

QuietLagoon (813062) | more than 4 years ago | (#33917992)

His presentation [ted.com] .

Re:From his February 2010 TED visit (1)

chichilalescu (1647065) | more than 4 years ago | (#33918184)

I saw a similar presentation he gave in 2007. We need more people like him.

Re:From his February 2010 TED visit (1)

Chelmet (1273754) | more than 4 years ago | (#33918262)

I'm surprised.

I listened to that TED podcast a few weeks ago, I found it really interesting, but I was driving at the time, and once getting home it had completely slipped my mind to read more in to it.

His presentation was excellent, and it didn't occur to me that he was nearly that old.

Re:From his February 2010 TED visit (2, Interesting)

RDW (41497) | more than 4 years ago | (#33918296)

Thanks! More years ago than I care to remember (about the same time I was playing around with Fractint from a covermount floppy of some magazine) the great man came to our university to give a talk. Stupidly I didn't join the queue early enough and got stuck in an overflow room (the maths guys hosting his visit hadn't calculated the demand correctly). Still cool to hear him talk, though. I remember the Genesis Device got a mention:

http://vimeo.com/5810737 [vimeo.com]
http://www.youtube.com/watch?v=NM1r37zIBOQ [youtube.com]

Testimony (4, Interesting)

kale77in (703316) | more than 4 years ago | (#33917998)

I was in year nine (mid-high-school) in country Australia, when my grandmother gave me a subscription to Scientific American; on the front of one of the first issues was a Mandelbrot set. I put the pseudocode into Atari Basic on my trusty 800XL (1.86kHz), and it produced a 40x40 graph of the set in just on 6 hours. It's been one of my standard learn-a-new-language exercises ever since, and the single thing I love the most about mathematics.

Re:Testimony (1)

Mojo66 (1131579) | more than 4 years ago | (#33918102)

Yeah I read the same issue ("Spektrum der Wissenschaft" here in Germany) and quickly wrote a programm for my Apple ][, only to be surprised of how slow it was. Later, I re-wrote the same program in 6502 Assembler using Merlin, and it took about 5 minutes to fill the 280x192 screen. Then I rewrote the program to directly print the Mandelbrot set on an Epson 800 printer in ESC/P on 15 DIN A4 sheets, spanning 1x1m. The program ran for 1 week on a Saturn 3.5 MHz accelerator card.

Re:Testimony (1)

Nethead (1563) | more than 4 years ago | (#33918454)

Yep, that's how I learned Asm on the C64. Kept moving parts of the BASIC code to machine. I leaned a lot about optimization that way, stuff that has stayed with me for decades.

Re:Testimony (1)

fraktus (632342) | more than 4 years ago | (#33920276)

When I interview developers I show then a shader that draws the Mandelbrot fractal and I ask them what language do you think is this code written and of course what do you think is going to be displayed by this so small code loop, this is leading me to very interesting discussion with the candidate!

Re:Testimony (2, Informative)

butlerm (3112) | more than 4 years ago | (#33918558)

I put the pseudocode into Atari Basic on my trusty 800XL (1.86kHz)

I think you mean something megahertz. A one kilohertz computer wouldn't be good for much of anything. The Apple II, C-64, Atari 400/800, etc. all ran 1 Mhz 6502 CPUs at approximately 1 Mhz, somewhat more than that in the Atari case.

Re:Testimony (1)

MillionthMonkey (240664) | more than 4 years ago | (#33918952)

When I was ten my first computer was a ZX81 and in SLOW mode (w/ no screen flicker on each keystroke) it ran at 800 kHz. It executed BASIC code about as fast as you could read it. Seriously- I remember figuring this out and realizing I was FORCED to learn ASM on the Z-80. Then I learned it and was AMAZED that I could make an ASM loop run 65536 times in less than a second, but I couldn't think of anything cool to do in the loop body.

Re:Testimony (2, Interesting)

mikael (484) | more than 4 years ago | (#33919034)

I remember those days - reading his book on the "Fractal complexity of nature" was a real inspiration. It was strange to realize that snowflakes, ice crystallisation, mountain terrain, the outlines of coastlines, branching of trees and lightning, aggregation of soot particles, growth of coral and seashells, periodicity of landslides and earthquakes could all be modelled by fractals.

Some of those simulations could be done within seconds on an Atari(XL) or other home computer. Others took hours like the Mandelbrot set as well as others like John Conway's Game of Life - the 1D version was a bit faster. Spending three Summer evenings running a 6502 implementation of John Conway's "Life" program on a for all 1000+ generations on a 160x80 grid. I always remember the stars in the twilight sky at that time looked just like the cover of the 1978 BYTE magazine.

I feel a little bad about this (1)

lula-vampiro (1322203) | more than 4 years ago | (#33918016)

but the first thing I thought was, "damn, that one Jonathan Coulton song is going to be really confusing whenever he performs it now." Seriously, though, it's sad that he's dead but I'm happy to reflect that he had the kind of full, accomplished life for which we all hope.

Re:I feel a little bad about this (3, Interesting)

Burpmaster (598437) | more than 4 years ago | (#33918356)

I feel a little bad about this but the first thing I thought was, "damn, that one Jonathan Coulton song is going to be really confusing whenever he performs it now."

Can't be worse than immediately thinking "I must post the best yo dawg joke ever." You know, he put the Mandelbrot Set in the Mandelbrot Set, so we can explore it while we explore it.

From this day forward, this recursive meme ought to be associated with Mandelbrot. After all, he put something inside itself infinitely many times long before Xzibit did so once.

Fractint (1)

Bazman (4849) | more than 4 years ago | (#33918154)

Is there anything better than Fractint now? I too played with it for ages on a clunky old IBM PC with clicky keyboard and Windows 2 (although Fractint ran in DOS though, I think, and necessitated misc tweaking with graphics drivers to make it work, you kids don't know how lucky you are...)

Re:Fractint (4, Informative)

paskie (539112) | more than 4 years ago | (#33918188)

The best I know is GNU XaoS. It can do real-time zooming (it did fine even on my old P133!) and features plenty of settings and fractal equations. I know there are perhaps better programs nowadays that let you easily write custom equations, scripts for 3D fractals and whatnot, but AFAIK none is free and/or supports Linux well.

Re:Fractint (1)

mark-t (151149) | more than 4 years ago | (#33918508)

Doesn't Xaos use a limited precision though, creating a rather hard limit on how far one can zoom in, even though performance and resources may not necessarily be getting taxed?

Re:Fractint (1)

MillionthMonkey (240664) | more than 4 years ago | (#33920172)

I used to think this was a big deal, but I decided not to bother with arbitrary precision recently just because it sacrifices performance too much at ordinary zoom levels (unless you aren't lazy). FRACTINT implemented it adaptively, but it was still like hitting a wall.

The thing is, there's fundamentally nothing you can see at a high zoom level that doesn't look very similar to features visible somewhere at lower magnification. After you zoom in a dozen times, the floating point arithmetic bugs are suddenly the most interesting things you see.

Re:Fractint (0)

Anonymous Coward | more than 4 years ago | (#33919154)

ZoneXplorer by Elena Novaretti, available for classic Amiga OS and PowerUp Amiga (PPC) (I think), and MorphOS (and maybe other OS, not sure), is a fantastic fractal generator. No real-time zooming, but you can do some things with it that are very unique. Not sure where her home page is these days.

Re:Fractint (0)

Anonymous Coward | more than 4 years ago | (#33918204)

Fractal eXtreme? It's not as full-featured as FractInt but the UI is about a million times better. On a fast multi-core CPU (64-bit version especially) you can real-time zoom without pausing to a magnification of a googol:1 or more. The maximum magnification is much higher than that, but eventually you have to start waiting for the frame to render before you can choose your zoom target. Mouse-wheel, double-click, or hold down 'I' and point at an interesting area.

It's amazing how much faster computers are now, but the animated zoom, rendering from the midde instead of the top, and the all-important lower-res early passes also help keep it interactive when it's not instantaneous. FractInt was always cool, but too clunky for my tastes. (http://www.cygnus-software.com/)

Re:Fractint (1)

dserpell (22147) | more than 4 years ago | (#33918236)

Is there anything better than Fractint now? I too played with it for ages on a clunky old IBM PC with clicky keyboard and Windows 2 (although Fractint ran in DOS though, I think, and necessitated misc tweaking with graphics drivers to make it work, you kids don't know how lucky you are...)

You have the open-source "xaos" http://xaos.sf.net/ [sf.net] for a fast interactive fractal exploring and "Fraqtive", http://fraqtive.mimec.org/ [mimec.org] for a beautiful view generator. Also, there are new versions of fractint, but the UI is really outdated. Wikipedia has a list with a few more, at http://en.wikipedia.org/wiki/Fractal-generating_software [wikipedia.org]

Re:Fractint (1)

gregbaker (22648) | more than 4 years ago | (#33918248)

I just looked around the Ubuntu repositories for nostalgia's sake and found Fraqtive (http://fraqtive.mimec.org/). It looks pretty slick, uses multiple cores and SSE instructions to get you there faster, Win/Mac/Linux.

The last 3 minutes of exploring would have taken weeks on my Apple II.

Re:Fractint (1)

sznupi (719324) | more than 4 years ago | (#33918298)

Not exactly interactive, but still quite nice concept: http://en.wikipedia.org/wiki/Electric_Sheep [wikipedia.org]

Re:Fractint (1)

illumastorm (172101) | more than 4 years ago | (#33918478)

Aren't electric sheep the objects androids dream about?

Re:Fractint (1)

sznupi (719324) | more than 4 years ago | (#33918582)

...or PCs, it would seem.

Anyway, I just remembered one more shiny: http://www.cs.caltech.edu/~keenan/project_qjulia.html [caltech.edu] (in "Ports" few variants which might be more to your liking; this page [skynet.be] includes also "2D" mandelbrot and julia gpu viewer)

Re:Fractint (1)

Sulphur (1548251) | more than 4 years ago | (#33919180)

They think about electric sheep to go to sleep, but once asleep they dream about the electric jeep and weep.

Re:Fractint (1)

ptrace (1078855) | more than 4 years ago | (#33918704)

Fracatal eXtreme [www.cygnus-software]

Re:Fractint (1)

Randle_Revar (229304) | more than 4 years ago | (#33918992)

KaiRo made a SeaMonkey extension Mandelbrot explorer. Probably works in FF as well.

That it was only on a 4-color CGA did not deter me (1)

commodore64_love (1445365) | more than 4 years ago | (#33918206)

Poor guy. Those of us with our $150 or $300 Commodores and Ataris ran the fractals in gorgeous 16 or 128 colors. Perfect example of how cheaper products can be better than those $100 PCs or $3000 Apples.

I got bored with fractals quickly. The odd shapes they generated were pretty, but I found the graphix demos generated by pirate groups to be far more interesting.

Re:That it was only on a 4-color CGA did not deter (1)

commodore64_love (1445365) | more than 4 years ago | (#33918232)

Correction:

>>>$1,000 PCs

RIP (1)

dln385 (1451209) | more than 4 years ago | (#33918228)

Benoit Mandelbrot practically invented a new field of mathematics that we now use for everything from measuring the size of forests to identifying cancer in its early stages. He was the best of mathematicians.

Eight months ago he gave a ted talk describing his work [ted.com] . If you want to explore fractals for yourself, I recommend GNU XaoS [u-szeged.hu] for all platforms.

Another Mandelbrot - Clarke connection (2, Interesting)

sznupi (719324) | more than 4 years ago | (#33918268)

I first learned of the Mandelbrot set while watching one of Clarke documentaries, Fractals: the colours of infinity - very nicely done; very inspiring(*), as was the performance (despite its shortness) of Benoit Mandelbrot himself.

Now both gone :/

(*)perhaps too inspiring - I still wait for something like that fractal compression of parrot picture.

He didn't really die, you know (4, Insightful)

roman_mir (125474) | more than 4 years ago | (#33918300)

if you look closer, you'll realize that he didn't die, it's just he became too big for us to see.

Re:He didn't really die, you know (1)

istartedi (132515) | more than 4 years ago | (#33918708)

1: No, look he's over there.
2: Where?
1: Between this and that.
2: OK, between this and that. There's a thing between this and that.
1: Yes, look between this and that other thing.
2: OK, there's something there is that him?
1: No, look between this and that. Keep looking...

Re:He didn't really die, you know (1)

Randle_Revar (229304) | more than 4 years ago | (#33919084)

>begs the question

You know, I have given up on this one. Not only is it too late to save it, it is a horrible translation in the first place. Nowadays I prefer to use the Latin: petitio principii. After all we Latin for other logical fallacies, like ad hominem and non sequitur

As for "whom" I don't care one way or the other. "intensive purposes" is just horrible, though. It sounds like nails on a chalkboard.

Re:He didn't really die, you know (1)

roman_mir (125474) | more than 4 years ago | (#33919510)

well, look at the rest of that comment. Did it make any sense at all from top to bottom?

Thus, of-course, it's "intensive purposes" and "begs question", where there was no begging of any question obviously.

Re:He didn't really die, you know (1)

Randle_Revar (229304) | more than 4 years ago | (#33919720)

Oh, I understood what he was doing.

Mandelbrot plot (5, Funny)

JohannesJ (952576) | more than 4 years ago | (#33918316)

In school we had to plot Mandelbrots. Now Mandelbrot has a plot of his own.

damn you rss! (5, Funny)

Anonymous Coward | more than 4 years ago | (#33918348)

http://news.slashdot.org/story/10/10/16/1446231/Benoit-Mandelbrot-Dies-At-85?from=rss

rss takes another victim...

An Inspiration (3, Insightful)

hoover (3292) | more than 4 years ago | (#33918430)

I think those pictures he came up with first inspired an entire generation of would-be computer scientists, maths geeks, physicists and Scientific American readers. How such a simple iteration could render those fascinating patterns even on a 2d grid, remains to this day one of the big mysteries. R.I.P. Benoit, I hope you'll finally be able to make sense of the fractal nature of things from up / down there!

I'll miss the guy (4, Interesting)

line-bundle (235965) | more than 4 years ago | (#33918450)

I met the guy personally at least 4 times in the last 5 years. He was great to get along with and not aloof at all for all his successes.

I'm currently following up on is work in finance (stable distributions).

May he RIP, and may his family consider him resting.

Fractals.. a gateway drug to more complex models (5, Interesting)

seandoyle44 (1835628) | more than 4 years ago | (#33918502)

I remember the Scientific American with the Mandelbrot set on the cover - it was a huge influence on my life. I was working as a research assistant at the Federal Reserve Board in DC and was losing interest in mathematical modeling as a way to understand anything in the real world. Most of the models I was dealing with were linear or mostly linear. When I read the article at first I thought it was some cheap trick or approximation... but gradually I realized it was different than anything I had seen before. So - being a rational, optimizing actor I then left the field of economics .. the most utility-maximizing decision I ever made :-) Since then I've always viewed fractals as a gateway drug to more complex models of the universe. So many processes unfold over time; fractals are just one of the ways to get a glimpse of what might be going on. Thanks Dr. Mandelbrot!

Mandelbrot Set (4, Insightful)

dirkson (1085087) | more than 4 years ago | (#33918534)

He gave us order out of chaos; he gave us hope where there was none. And his geometry succeeds where others fail. Mandelbrot's in heaven.

Re:Mandelbrot Set (0)

Anonymous Coward | more than 4 years ago | (#33920266)

He gave us chaos out of order. Fixed that for you.

Was there ever a real-time viewer... (1)

mark-t (151149) | more than 4 years ago | (#33918536)

... that was not merely limited to single or even double precision?

Re:Was there ever a real-time viewer... (1)

wildsurf (535389) | more than 4 years ago | (#33918682)

Yes, KPT Fraxplorer in the KPT5 suite of Photoshop plug-ins implements 1024-bit math to zoom in far deeper than double-precision allows.

Re:Was there ever a real-time viewer... (2, Informative)

spitzak (4019) | more than 4 years ago | (#33918886)

He asked for "real time".

I would suspect the switch from hardware doubles to software arbitrary-precision produces many orders of magnitude of slowdown so the answer is no.

Math and youth (5, Interesting)

ortholattice (175065) | more than 4 years ago | (#33918586)

Defying the notion that mathematicians are over the hill at age 30, Mandelbrot made his fractal breakthroughs when he was in his 50s. It gives the rest of us some hope. :)

Re:Math and youth (0)

Anonymous Coward | more than 4 years ago | (#33920594)

Inspiring. Let us never stop exercising that muscle we call the brain*, and maybe we'll leave the world a little richer with knowledge.

* I had a buddy who, upon learning that the the accident risk to new motorcyclists is the highest in the first several months of riding, said he would get his license then wait six months before starting to ride.

Fractint Rocks (1)

pcjunky (517872) | more than 4 years ago | (#33918680)

I spent many hours exploring fractals with that software. Though I had a little better graphics (EGA). Fond memories.

A great mathematician is no more... (2, Insightful)

farrellj (563) | more than 4 years ago | (#33918710)

I, too, used Fract386, which became Fractint....I worked at a computer store in Toronto, and we used to sell so many NEC Multi-Sync monitors with ATI's VGA Wonder card based upon showing Fractint on it!

Through someone on I met on LJ, I was able to get a "autographed mandelbrot", basically a color print out of part of the Mandelbrot set, autographed by the now, late, great Benoit Mandelbrot. Although I never got to meet him, he discovery has given much beauty to my life.

ttyl
          Farrell

Thank you Mandelbrot! (3, Insightful)

KingAlanI (1270538) | more than 4 years ago | (#33918730)

Fractals were how this non-artist got his art credit in high school with style. :)

Baruch Dayan Haemes (1)

bennyp (809286) | more than 4 years ago | (#33918752)

Upon receiving sad tidings, a Jew recites the blessing "Blessed is the True Judge" The Omnipresent should comfort the Mandelbrot family in the Gate of Zion's Mourners in Jerusalem.

Colors of Infinity (0)

Anonymous Coward | more than 4 years ago | (#33918906)

To commemorate this, we should all re-watch Colors of Infinity: http://www.youtube.com/watch?v=qB8m85p7GsU

This is a good chance to remind y'all (4, Interesting)

symbolset (646467) | more than 4 years ago | (#33918934)

Many of the people who have discovered things great and small that astonish and delight are still living. It's not too late to look them up on the internet and personally thank them.

So much to say (1)

muridae (966931) | more than 4 years ago | (#33919080)

My feelings at his passing are both too real and too complex to explain in plane terms.

Seen it all (5, Funny)

dgriff (1263092) | more than 4 years ago | (#33919378)

ran it for long periods of time [...] exploring the beautiful world

Yeah, but when you've seen one part of the Mandelbrot set, you've seen it all.

Farewell (1)

Fractal Dice (696349) | more than 4 years ago | (#33919868)

The boundaries of his life were filled with many twists and turns.

Check out 3D fractals (2, Interesting)

maktlaust (1545855) | more than 4 years ago | (#33920084)

Zooming into a Mandelbox, with weird music: http://vimeo.com/13886600 [vimeo.com]

My first program... (2, Interesting)

curious.corn (167387) | more than 4 years ago | (#33920264)

... back in uni - gwbasic I think - was a Mandelbrot set renderer. We were just starting with Mathematical Analysis and the first real struggles with imaginary numbers, sequences, series and limits. I guess messing around with it cost me an exam session, but it was way much more fun than rote theorems (later Profs were good, not that first class though ;( )

RIP

CG procedurals (2, Interesting)

MobileTatsu-NJG (946591) | more than 4 years ago | (#33920434)

A few years ago it was popular to make CG images of starships with a procedural/fractal nebula in the background. I used to make comments like: "The Enterprise is investigating the Mandelbrot Nebula", but nobody I know of ever got it.

Inspiring life (1)

cuby (832037) | more than 4 years ago | (#33920446)

At least for me... I first read something about him, in my freshman year in college, in the book Caos, by James Gleick http://www.amazon.com/exec/obidos/ASIN/0140092501/jamesgleick [amazon.com] . To this day I remember him with the utmost consideration. I hope he had a happy life. I'll never forget his work... He was one of the great scientists of our time.
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