On Fractals and Exegesis

Dawn Gilpin
14 min readJul 21, 2022


This is something I wrote back in the day for a now-defunct website called Tea At the Ford (TATF), run by my friend macha. Actually, this was written before the site existed, when we were just a mailing list. macha had set up a little exercise for anyone who wanted to play, but unfortunately I don’t remember the details. I only remember that our mission, if we chose to accept it, was to start with a piece of dialogue from the BtVS episode Dead Things (6.13) (referred to as “Exhibit A” below) and do… something. There’s a reference to “what it looks like if you turn it over,” meaning reversing the roles, but I don’t remember exactly how the pieces were supposed to fit together.

At this point in time, not long after the series ended and before S5 of Angel aired, I had only watched S4 of the latter so was missing some key bits. Everyone, however — even an obsessive spoilerphobe like myself — knew that Spike would be joining the cast of the latter, though.

Anyway, the conversation surrounding the exercise is sadly lost to the mists of time, but my main contribution to it is below. I recently came across some of my TATF writings and wanted to put them somewhere, for reference. Starting here.

The first thing I was reminded of when I saw this exercise was a fractal pattern. I don’t want to bore anyone with excess detail, but just to briefly explain what I’m talking about: fractal mathematics are a specific type of nonlinear calculation that uses recursive iterations to reveal patterns that remain invariable regardless of scale. These iterations produce, over time, unpredictable but recognizable patterns.

Translation into plain English: think of how water droplets self-organize into regular and identifiable patterns, yet it is impossible to predict exactly what form a cloud will take. This holds true whether we are looking at the steam from a teapot, eyeing a storm cloud in the sky, or viewing satellite photographs of global weather patterns: the scale may change, but the underlying phenomenon remains the same.

Fractal equations produce graphics that show how very slight alterations in interactions among the elements of a complex system will, over time, develop into patterns that evolve in a nonlinear yet regular fashion. Since they portray a process that is the result of evolution, fractals also incorporate the element of time, and show how the history of a given system plays a role in reaching its present state. Fractal patterns — which can be very beautiful in their own right — are like time-lapse photographs of a system’s development.

One way in which the concept of fractals has been applied to social systems is in communication, specifically patterns of speech and conversation. We tend to have the same conversations over and over, in many areas of our life — except they’re not really exactly the same. Something is always different: who says what, a slight change in wording, the setting, the tone. Maybe the words stay the same, but the meaning changes because of things that have happened in the interim. All of these are tiny, incremental variations that move the pattern forward in a process of change that can be invisible, or nearly so, when we’re inside it, but shifts clearly into focus with the perspective of distance (physical distance or time, telescope or hindsight).

Which brings us back to Buffy, and the exercise. Starting with Exhibit A, the excerpt from Dead Things:

Spike: What do you think you’re doing?
Buffy: The right thing. For once.
Spike: Sorry, luv. Can’t let you do that.

Of course, to really do this properly, I should go back through past seasons and look at all the similar conversations that have taken place over the years. Doing this for every segment of the exchanges used in the exercise would probably show some very interesting developments. Well, you know, it’s cooled off a bit here, but not that much (plus, this post would be book-length, and finished sometime around Christmas). Here are a few examples, though, that might show us a bit of a fractal pattern, based on some of the times Buffy has talked about doing the right thing. I hope this will at least give you an idea of the kind of thing I have in mind, so I can use some shorthand on the rest.

From Inca Mummy Girl (episode 2.04)
Buffy: She was gypped. She was just a girl, and she had her life taken away from her. I remember how I felt when I heard the prophecy that I was gonna die. I wasn’t exactly obsessed with doing the right thing.
Xander: Yeah, but you did. You gave up your life.
Buffy: I had you to bring me back.

From Surprise (episode 2.13)
Buffy: I mean, ‘want’ isn’t always the right thing to do. To act on want can be wrong.
Willow: True.
Buffy: But… to not act on want… What if I never feel this way again?
Willow: Carpe diem. You told me that once.
Buffy: ‘Fish of the day’?
Willow: Not carp. Carpe. It means ‘seize the day.’
Buffy: Right. I… I think we’re going to. Seize it. Once you get to a certain point, then seizing is sort of inevitable.
Willow: Wow…
Buffy: Yeah.

From Faith, Hope & Trick (episode 3.03)
Buffy: Faith, first rule of slaying: don’t die. You did the right thing. Okay? You didn’t die.

From Amends (episode 3.10)
Buffy: It’s just so frustrating. I’m trying to do the right thing and stay away from him and get over it, and then boom, there he is. I just want a nice, quiet Christmas vacation.

From Consequences (episode 3.15)
Faith: So, you gonna rat me out? Is that it?
Buffy: Faith, we have to tell. I can’t pretend to investigate this. I can’t pretend that I don’t know.

Faith: Oh, I see. But you can pretend that Angel’s still dead when you need to protect him.
Buffy: I am trying to protect you. Look, if-if we don’t do the right thing, it’s only gonna make things worse for you.
Faith: Worse than jail for the rest of my young life? No way!
Buffy: Faith, what we did was…
Faith: Yeah. We. You were right there beside me when this whole thing went down. Anything I have to answer for, you do, too. You’re a part of this, B. All the way.

Buffy and “the right thing to do” have quite a history. She’s rebelled against it, tried to do it, dithered between it and what she really wants, encouraged others to do it, and had it turned against her. All before this conversation in Dead Things takes place. Most of all, as Slayer, she is expected to Do The Right Thing all the time. That’s what those hero types do, right? She has to be perfect, and if she’s not perfect, she’s defective. She Came Back Wrong.

Everything is hard and bright, and she wants to die (going right against the first rule of slaying), and she is irresistibly drawn to someone she knows to be Evil (wanting something doesn’t mean it’s the right thing, fish of the day aside). If she withdraws from her friends and family (who were there to bring her back yet again after she did the right thing, never letting her just be done with it), and the only person she can stand to be around is a completely lame neutered vampire who cheats at kitten poker (even though she tries to do the right thing and stay away from him and get over it, but then she turns around and boom there he is), what does that say about her?

Time to turn herself in, just like she tried to do with Faith. It’s something she feels very strongly about:

Spike: You’re not going in there.
Buffy: I have to do this. Just let me go.
Spike: I can’t. […] You are not throwing your life away over this.
Buffy: It’s not your choice.

I know this isn’t really a Buffy conversation, but as I mentioned in the thread about AU/APOV episodes, I think the body swap in Season 4 is intended to give not only Faith, but also the audience, a glimpse of what it’s like to be Buffy. Consider this a fractal twist in which the players change but the conversation stays more or less the same:

From Who Are You? (episode 4.16)
Riley: I don’t want you risking —
Faith: (sharply) Don’t tell me what to do! (forced conviction) I’m Buffy. I have to do this.
Riley: (nods) Then I’m coming with. (She considers this for all of one second and lightly hits him in the side. His response is immediate as he clutches his still healing wound.)
Riley: (painfilled) Oww!

Stubborn girl, our Buffy. Even when she’s really not. Buffy, that is. Once she makes up her mind about something, it’s not easy to sway her. She likes to make her own decisions.

What if we switch it around a bit, so that instead of begging to be let go, Buffy’s begging someone to make her stay?

From Lovers’ Walk (episode 3.08)
Angel: She wants you to get out.
Buffy: Someplace a little less Hellmouthy. (nods) She has a point. Y’know, but there are reasons to stay, too.
Angel: What are they?
Buffy: Um… you know, there’s my Slayer duties, obviously. What do you think I should do?
Angel: As a friend, I… I think that you should leave. This is a good opportunity for you.
Buffy: Yeah. It’s not like there’s any great thing keeping me here. Thanks for the advice. It’s another perspective to consider.
Angel: Where are you going? You just got here. It’s early.
Buffy: Yeah, well, my mom starts worrying a lot earlier these days. I’ll stop by soon.

Jumping for a moment here to the flip side of Exhibit A (hey, this is all about the nonlinearity, right?): what it looks like if you turn it over.

Just another fractal twist, this, but it can lead to a whole new pattern of its own:

Buffy: What do you think you’re doing?
Spike: The right thing. For once.
Buffy: Sorry, luv. Can’t let you do that.

Buffy likes to make her own decisions, but she’s not always keen on others making theirs, especially as they affect her. Also because, funnily enough, they so often seem to be about men leaving her.

From Tabula Rasa (episode 6.08)
Buffy: But why now? Now that you know where I’ve been, what I’m going through?
Giles: Now more than ever. The temptation to give up is gonna be overwhelming, and I can’t let-
Buffy: So I won’t! No giving up. You can be here, and I can still be strong.
Giles: Buffy, I’ve thought this over … and over. I believe it’s the right thing to do.
Buffy: You’re wrong. (storms off)

Now, back to the fun part of Exhibit A:

Spike: I love you.
Buffy: No, you don’t.
Spike: You think I haven’t tried not to?
Buffy: (punches him) Try harder.

And the flip version, backing up a tad:

Buffy: You’re not going in there.
Spike: I have to do this. Just let me go.
Buffy: I can’t. I love you.
Spike: No, you don’t.
Buffy: You think I haven’t tried not to?
Spike: (punches him) Try harder.
Buffy: You are not throwing your life away over this.
Spike: It’s not your choice.

Oh, the conversations, how they repeat over and over again, varying ever so slightly…

From The Prom (episode 3.20)
Angel: (grabs her arm) I’m sorry. Buffy, you know how much I love you. It kills me to say this.
Buffy: Then don’t. Who are you to tell me what’s right for me? You think I haven’t thought about this?
Angel: Have you, rationally?
Buffy: No. No, of course not. I’m just some swoony little schoolgirl, right?
Angel: I’m trying to do what’s right here, okay? I’m trying to think with my head instead of my heart.
Buffy: Heart? You have a heart? It isn’t even beating!
Ange: Don’t.
Buffy: Don’t what? Don’t love you? I’m sorry. You know what? I didn’t know that I got a choice in that. I’m never gonna change. I can’t change. I want my life to be with you.
Angel: I don’t.

From Amends (episode 3.10) (sorry for the extra long quote, but it felt necessary)

Buffy: I don’t have time to explain this. You just have to trust me. That thing that was haunting you…
Angel: It wasn’t haunting me. It was showing me.
Buffy: Showing you?
Angel: What I am.
Buffy: Were.
Angel: And ever shall be. I wanted to know why I was back. Now I do.
Buffy: You don’t know. Some great evil takes credit for bringing you back and you buy it? You just give up?
Angel: I can’t do it again, Buffy. I can’t become a killer.
Buffy: Then fight it.
Angel: It’s too hard.
Buffy: Angel, please, you have to get inside.
Angel: It told me to kill you. You were in the dream. You know. It told me to lose my soul in you and become a monster again.
Buffy: I know what it told you. What does it matter?
Angel: Because I wanted to! Because I want you so badly! I want to take comfort in you, and I know it’ll cost me my soul, and a part of me doesn’t care. Look, I’m weak. I’ve never been anything else. It’s not the demon in me that needs killing, Buffy. It’s the man.
Buffy: You’re weak. Everybody is. Everybody fails. Maybe this evil did bring you back, but if it did, it’s because it needs you. And that means that you can hurt it. Angel, you have the power to do real good, to make amends. But if you die now, then all that you ever were was a monster. Angel, please, the sun is coming up!
Angel: Just go.
Buffy: I won’t!
Angel: What, do you think this is simple? You think there’s an easy answer? You can never understand what I’ve done! Now go!
Buffy: You are not staying here. I won’t let you!
Angel: I said LEAVE! […] Am I a thing worth saving, huh? Am I a righteous man? The world wants me gone!
Buffy: (tearfully) What about me? I love you so much… And I tried to make you go away… I killed you and it didn’t help. (crying) And I hate it! I hate that it’s so hard… and that you can hurt me so much. I know everything that you did, because you did it to me. Oh, God! I wish that I wished you dead. I don’t. (whispers) I can’t.
Angel: Buffy, please. Just this once… let me be strong.
Buffy: Strong is fighting! It’s hard, and it’s painful, and it’s every day. It’s what we have to do. And we can do it together. But if you’re too much of a coward for that, then burn. If I can’t convince you that you belong in this world, then I don’t know what can. But do not expect me to watch.

We can’t choose whom we love, we can’t force ourselves to stop loving. We can’t make others stop loving us, and that can be the hardest thing of all, especially when we know don’t deserve it, when we’re Wrong. There is one constant amid all the upheaval, though: you always hurt the one you love.

Buffy and Angel, Buffy and Spike. Spike becomes Buffy; Buffy, Angel. Sometimes what we want isn’t the right thing, and it’s hard to tell the difference. Like Angel does of her, she dreams of taking comfort in Spike, and she dreams of killing him. Which is the right thing? Which is what she wants? They can’t be the same thing anymore, because she Came Back Wrong. Buffy wants Spike, but that’s just another sign she’s wrong. So much easier to give up, turn herself in, go to jail, step outside the hard bright world and console herself that she’s done the right thing, for once.

Spike won’t let her, he never lets her get away from herself. Spike is to Buffy as Buffy was to Angel, except it’s all confusing because isn’t he Evil? And isn’t she Good? Is she a righteous woman, worth saving? But how can she be saved by an evil, soulless thing? When did the lines get all blurry? From inside the fractal, the patterns have shifted ever so gradually, imperceptibly, but stepping back from the single water droplet we see a cloud. Step back even farther, and we see the entire storm front. A regular apocalypse, it is.

So, we’ve had the Conversation in its various permutations over the years, changing settings, changing tone, changing sides. The Sunnydale teapot has produced its tempest, and of course the Conversation comes ‘round again. Here, though, the pattern has evolved to a new level.

Spike: Go on, then.
Buffy: No, you’ve done enough. You could still —
Spike: No. You beat them back. It’s for me to do the cleanup.
Faith: (on stairs) Buffy, come on.
Spike: Gotta move, lamb. I think it’s safe to say that school’s out for bloody summer.
Buffy: Spike.
Spike: I mean it. Gotta do this. (The pit is collapsing inward.)
Buffy: (she entwines her hand with his and he grasps it tightly. Flames come from it.) I love you.
Spike: No you don’t. But thanks for saying it. (She’s crying. More stuff falls. She takes her hand back.) Now go. (to himself) I want to see how it ends.

Finally, there is mutual respect, and self-respect. Spike knows what he has to do: it’s the right thing, and he wants it. Buffy doesn’t it want it, but she understands that it’s the right thing, and she is willing to let him go. It’s the Chinese proverb co-opted by Hallmark, sadly acquiring a topping of extra cheese: if you love something, set it free. No more hurting, no more selfishness, no more self-flagellation. The bond that was forged in Becoming has now Become, forged in flame, complete with scrubbing bubbles.

Complex systems are never static. Stasis is the same as death, life is never-ending change. Tiny fractal changes that build up to move mountains and sink whole towns into the Hellmouth. Angel is stuck with the curse that keeps him tightly locked in a static world, unable to truly change, more dead than the rest of the undead. Certainly more dead than Spike, whose own words about demons never changing certainly didn’t apply to himself.

In complexity terms, the system of the Buffyverse has reached the edge of its attractor basin, come to a bifurcation point, and is ready to leap into a whole new dimension. Buffy is free of her burdens as Chosen One and can work on her confectionery skills. What remains to be seen is how a strange attractor (a seemingly random force for change that produces unpredictable results) such as Spike will affect the static world of Angel. I’m missing a huge chunk of reference material, so it’s hard for me to really say much about the AtS world, but it seems that Angel himself has remained largely outside the rest of the system of his world, as those around him evolve. He’s not part of the fractal patterns that surround him.

The reason I’m wondering about this here, where it may seem out of context, is because of The Conversation: will we see the missing variations, the ones between Spike and Angel? And if so, will Angel be doomed to play the same part as before, and Spike the one who saves (or tries to save) him from himself? There’s a possibility, I’m thinking, that this might even be a major theme, rather than just a scene or two. Of course, if Angel somehow manages to wrench free of his static condition, he might even be able to have The Conversation from both sides, which would be an earth-shattering (and possibly dimension-shattering) development.

Do I actually have a conclusion here? Not really. I’m not really big on conclusions, which has often been something of a problem. I know this wasn’t actually exegesis, because I don’t know how to do the fancy stuff, but it was a fun chance to point at things and say, “ooh, look at that!” and just sort of sit and marvel, without having to arrive at Point Z. So, consider us arrived at whatever point seems appropriate (I’m kinda partial to Q, myself), and most of all, consider me free to read the zillions of posts I’ve had to skip.
— Sat 2003.06.28 at 02:51 pm EST



Dawn Gilpin

Assistant dean for research @Cronkite_ASU. I eat complex systems for breakfast, supplemented by Buffy the Vampire Slayer & fabulous shoes.